Path Lines of Code metamath/valid/aime-1983-p9.mm 9 metamath/valid/aime-1984-p15.mm 15 metamath/valid/aime-1984-p5.mm 11 metamath/valid/aime-1987-p8.mm 9 metamath/valid/aime-1988-p3.mm 9 metamath/valid/aime-1988-p4.mm 11 metamath/valid/aime-1990-p2.mm 7 metamath/valid/aime-1991-p1.mm 11 metamath/valid/aime-1991-p6.mm 9 metamath/valid/aime-1994-p4.mm 9 metamath/valid/aime-1996-p5.mm 21 metamath/valid/aime-1997-p12.mm 9 metamath/valid/aimeI-2000-p7.mm 16 metamath/valid/aimeI-2001-p3.mm 15 metamath/valid/aimeII-2020-p6.mm 13 metamath/valid/algebra-2complexrootspoly-xsqp49eqxp7itxpn7i.mm 20 metamath/valid/algebra-2rootsintpoly-am10tap11eqasqpam110.mm 19 metamath/valid/algebra-2rootspoly-apatapbeq2asqp2ab.mm 12 metamath/valid/algebra-2varlineareq-xpeeq7-2xpeeq3-eeq11-xeqn4.mm 31 metamath/valid/algebra-3rootspoly-amdtamctambeqnasqmbpctapcbtdpasqmbpctapcbta.mm 25 metamath/valid/algebra-amgm-faxinrrp2msqrt2geq2mxm1div2x.mm 7 metamath/valid/algebra-amgm-prod1toneq1-sum1tongeqn.mm 10 metamath/valid/algebra-amgm-sqrtxymulxmyeqxpy-xpygeq4.mm 11 metamath/valid/algebra-amgm-sumasqdivbsqgeqsumbdiva.mm 10 metamath/valid/algebra-apb4leq8ta4pb4.mm 9 metamath/valid/algebra-binomnegdiscrineq-10alt28asqp1.mm 23 metamath/valid/algebra-manipexpr-2erprsqpesqeqnrpnesq.mm 14 metamath/valid/algebra-manipexpr-apbeq2cceqiacpbceqm2.mm 16 metamath/valid/algebra-sqineq-2at2pclta2c2p41pc.mm 31 metamath/valid/algebra-sqineq-2unitcircatblt1.mm 10 metamath/valid/algebra-sqineq-36azm9asqle36zsq.mm 25 metamath/valid/algebra-sqineq-4bap1lt4bsqpap1sq.mm 34 metamath/valid/algebra-xmysqpymzsqpzmxsqeqxyz-xpypzp6dvdx3y3z3.mm 11 metamath/valid/amc12-2000-p11.mm 29 metamath/valid/amc12-2000-p15.mm 10 metamath/valid/amc12-2000-p5.mm 20 metamath/valid/amc12-2001-p2.mm 18 metamath/valid/amc12-2001-p9.mm 28 metamath/valid/amc12a-2002-p1.mm 12 metamath/valid/amc12a-2002-p12.mm 6 metamath/valid/amc12a-2002-p21.mm 11 metamath/valid/amc12a-2003-p1.mm 25 metamath/valid/amc12a-2003-p24.mm 31 metamath/valid/amc12a-2003-p25.mm 9 metamath/valid/amc12a-2008-p15.mm 9 metamath/valid/amc12a-2008-p2.mm 9 metamath/valid/amc12a-2008-p4.mm 7 metamath/valid/amc12a-2008-p8.mm 11 metamath/valid/amc12a-2009-p15.mm 9 metamath/valid/amc12a-2009-p2.mm 7 metamath/valid/amc12a-2009-p25.mm 11 metamath/valid/amc12a-2009-p5.mm 9 metamath/valid/amc12a-2009-p9.mm 14 metamath/valid/amc12a-2010-p10.mm 15 metamath/valid/amc12a-2010-p11.mm 11 metamath/valid/amc12a-2010-p22.mm 8 metamath/valid/amc12a-2011-p18.mm 10 metamath/valid/amc12a-2013-p7.mm 11 metamath/valid/amc12a-2013-p8.mm 13 metamath/valid/amc12a-2015-p10.mm 12 metamath/valid/amc12a-2016-p2.mm 9 metamath/valid/amc12a-2016-p3.mm 9 metamath/valid/amc12a-2017-p2.mm 12 metamath/valid/amc12a-2017-p7.mm 11 metamath/valid/amc12a-2019-p21.mm 9 metamath/valid/amc12a-2019-p9.mm 11 metamath/valid/amc12a-2020-p13.mm 16 metamath/valid/amc12a-2020-p22.mm 8 metamath/valid/amc12a-2021-p7.mm 9 metamath/valid/amc12b-2002-p11.mm 13 metamath/valid/amc12b-2002-p3.mm 34 metamath/valid/amc12b-2002-p6.mm 12 metamath/valid/amc12b-2003-p17.mm 27 metamath/valid/amc12b-2003-p6.mm 43 metamath/valid/amc12b-2003-p9.mm 36 metamath/valid/amc12b-2004-p3.mm 53 metamath/valid/amc12b-2020-p5.mm 11 metamath/valid/amc12b-2021-p21.mm 8 metamath/valid/imo-1961-p1.mm 18 metamath/valid/imo-1962-p4.mm 9 metamath/valid/imo-1964-p1-1.mm 9 metamath/valid/imo-1964-p1-2.mm 8 metamath/valid/imo-1965-p1.mm 12 metamath/valid/imo-1966-p4.mm 10 metamath/valid/imo-1966-p5.mm 19 metamath/valid/imo-1967-p3.mm 13 metamath/valid/imo-1973-p3.mm 10 metamath/valid/imo-1974-p5.mm 13 metamath/valid/imo-1977-p5.mm 14 metamath/valid/imo-1978-p5.mm 9 metamath/valid/imo-1979-p1.mm 10 metamath/valid/imo-1984-p2.mm 13 metamath/valid/imo-1987-p4.mm 8 metamath/valid/imo-1987-p6.mm 12 metamath/valid/imo-1988-p6.mm 10 metamath/valid/imo-1990-p3.mm 9 metamath/valid/imo-1993-p5.mm 7 metamath/valid/imo-2006-p6.mm 10 metamath/valid/induction-divisibility-3div2tooddnp1.mm 32 metamath/valid/induction-divisibility-3divnto3m2n.mm 43 metamath/valid/induction-divisibility-9div10tonm1.mm 25 metamath/valid/induction-ineq-nsqlefactn.mm 37 metamath/valid/induction-seq-mul2pnp1.mm 51 metamath/valid/induction-sum-1oktkp1.mm 40 metamath/valid/induction-sum-odd.mm 28 metamath/valid/induction-sum2kp1npqsqm1.mm 33 metamath/valid/mathd-algebra-10.mm 7 metamath/valid/mathd-algebra-101.mm 9 metamath/valid/mathd-algebra-104.mm 9 metamath/valid/mathd-algebra-109.mm 11 metamath/valid/mathd-algebra-11.mm 12 metamath/valid/mathd-algebra-110.mm 9 metamath/valid/mathd-algebra-116.mm 10 metamath/valid/mathd-algebra-119.mm 11 metamath/valid/mathd-algebra-123.mm 11 metamath/valid/mathd-algebra-126.mm 11 metamath/valid/mathd-algebra-13.mm 10 metamath/valid/mathd-algebra-131.mm 13 metamath/valid/mathd-algebra-132.mm 11 metamath/valid/mathd-algebra-140.mm 12 metamath/valid/mathd-algebra-144.mm 15 metamath/valid/mathd-algebra-149.mm 7 metamath/valid/mathd-algebra-15.mm 8 metamath/valid/mathd-algebra-151.mm 28 metamath/valid/mathd-algebra-159.mm 34 metamath/valid/mathd-algebra-181.mm 10 metamath/valid/mathd-algebra-182.mm 8 metamath/valid/mathd-algebra-185.mm 8 metamath/valid/mathd-algebra-190.mm 7 metamath/valid/mathd-algebra-192.mm 23 metamath/valid/mathd-algebra-206.mm 13 metamath/valid/mathd-algebra-214.mm 10 metamath/valid/mathd-algebra-22.mm 7 metamath/valid/mathd-algebra-224.mm 7 metamath/valid/mathd-algebra-234.mm 9 metamath/valid/mathd-algebra-245.mm 36 metamath/valid/mathd-algebra-247.mm 18 metamath/valid/mathd-algebra-251.mm 14 metamath/valid/mathd-algebra-267.mm 11 metamath/valid/mathd-algebra-28.mm 10 metamath/valid/mathd-algebra-282.mm 10 metamath/valid/mathd-algebra-31.mm 40 metamath/valid/mathd-algebra-323.mm 9 metamath/valid/mathd-algebra-327.mm 9 metamath/valid/mathd-algebra-35.mm 9 metamath/valid/mathd-algebra-37.mm 11 metamath/valid/mathd-algebra-393.mm 7 metamath/valid/mathd-algebra-405.mm 9 metamath/valid/mathd-algebra-410.mm 10 metamath/valid/mathd-algebra-421.mm 16 metamath/valid/mathd-algebra-422.mm 5 metamath/valid/mathd-algebra-43.mm 12 metamath/valid/mathd-algebra-433.mm 8 metamath/valid/mathd-algebra-437.mm 14 metamath/valid/mathd-algebra-451.mm 5 metamath/valid/mathd-algebra-455.mm 17 metamath/valid/mathd-algebra-462.mm 7 metamath/valid/mathd-algebra-48.mm 9 metamath/valid/mathd-algebra-480.mm 12 metamath/valid/mathd-algebra-482.mm 14 metamath/valid/mathd-algebra-493.mm 8 metamath/valid/mathd-algebra-509.mm 7 metamath/valid/mathd-algebra-51.mm 11 metamath/valid/mathd-algebra-510.mm 11 metamath/valid/mathd-algebra-536.mm 7 metamath/valid/mathd-algebra-547.mm 9 metamath/valid/mathd-algebra-55.mm 9 metamath/valid/mathd-algebra-568.mm 8 metamath/valid/mathd-algebra-59.mm 9 metamath/valid/mathd-algebra-616.mm 9 metamath/valid/mathd-algebra-67.mm 9 metamath/valid/mathd-algebra-69.mm 11 metamath/valid/mathd-algebra-73.mm 13 metamath/valid/mathd-algebra-77.mm 12 metamath/valid/mathd-algebra-89.mm 8 metamath/valid/mathd-algebra-96.mm 14 metamath/valid/mathd-numbertheory-101.mm 7 metamath/valid/mathd-numbertheory-102.mm 7 metamath/valid/mathd-numbertheory-109.mm 8 metamath/valid/mathd-numbertheory-110.mm 12 metamath/valid/mathd-numbertheory-126.mm 12 metamath/valid/mathd-numbertheory-13.mm 14 metamath/valid/mathd-numbertheory-132.mm 7 metamath/valid/mathd-numbertheory-136.mm 9 metamath/valid/mathd-numbertheory-149.mm 7 metamath/valid/mathd-numbertheory-155.mm 7 metamath/valid/mathd-numbertheory-156.mm 8 metamath/valid/mathd-numbertheory-169.mm 7 metamath/valid/mathd-numbertheory-188.mm 14 metamath/valid/mathd-numbertheory-198.mm 7 metamath/valid/mathd-numbertheory-200.mm 7 metamath/valid/mathd-numbertheory-202.mm 7 metamath/valid/mathd-numbertheory-211.mm 8 metamath/valid/mathd-numbertheory-22.mm 10 metamath/valid/mathd-numbertheory-221.mm 7 metamath/valid/mathd-numbertheory-232.mm 16 metamath/valid/mathd-numbertheory-236.mm 7 metamath/valid/mathd-numbertheory-24.mm 7 metamath/valid/mathd-numbertheory-252.mm 7 metamath/valid/mathd-numbertheory-257.mm 9 metamath/valid/mathd-numbertheory-269.mm 7 metamath/valid/mathd-numbertheory-284.mm 10 metamath/valid/mathd-numbertheory-30.mm 7 metamath/valid/mathd-numbertheory-301.mm 8 metamath/valid/mathd-numbertheory-303.mm 7 metamath/valid/mathd-numbertheory-32.mm 7 metamath/valid/mathd-numbertheory-326.mm 9 metamath/valid/mathd-numbertheory-33.mm 10 metamath/valid/mathd-numbertheory-335.mm 9 metamath/valid/mathd-numbertheory-35.mm 7 metamath/valid/mathd-numbertheory-37.mm 7 metamath/valid/mathd-numbertheory-370.mm 9 metamath/valid/mathd-numbertheory-403.mm 7 metamath/valid/mathd-numbertheory-405.mm 17 metamath/valid/mathd-numbertheory-412.mm 11 metamath/valid/mathd-numbertheory-42.mm 14 metamath/valid/mathd-numbertheory-43.mm 10 metamath/valid/mathd-numbertheory-45.mm 7 metamath/valid/mathd-numbertheory-458.mm 9 metamath/valid/mathd-numbertheory-461.mm 8 metamath/valid/mathd-numbertheory-466.mm 7 metamath/valid/mathd-numbertheory-48.mm 10 metamath/valid/mathd-numbertheory-530.mm 11 metamath/valid/mathd-numbertheory-543.mm 7 metamath/valid/mathd-numbertheory-629.mm 9 metamath/valid/mathd-numbertheory-64.mm 10 metamath/valid/mathd-numbertheory-640.mm 7 metamath/valid/mathd-numbertheory-668.mm 16 metamath/valid/mathd-numbertheory-690.mm 12 metamath/valid/mathd-numbertheory-709.mm 10 metamath/valid/mathd-numbertheory-739.mm 7 metamath/valid/mathd-numbertheory-780.mm 13 metamath/valid/mathd-numbertheory-81.mm 7 metamath/valid/mathd-numbertheory-84.mm 7 metamath/valid/mathd-numbertheory-92.mm 9 metamath/valid/mathd-numbertheory-961.mm 7 metamath/valid/numbertheory-2dvd4expn.mm 9 metamath/valid/numbertheory-aneqprodakp4-anmsqrtanp1eq2.mm 11 metamath/valid/numbertheory-nckeqnm1ckpnm1ckm1.mm 10 metamath/valid/numbertheory-prmdvsneqnsqmodpeq0.mm 76 metamath/valid/numbertheory-sqmod3in01d.mm 8 metamath/valid/numbertheory-sqmod4in01d.mm 37 metamath/valid/numbertheory-sumkmulnckeqnmul2pownm1.mm 8 metamath/valid/numbertheory-xsqpysqintdenomeq.mm 46