MathDB

10.3

Part of VMEO IV 2015

Problems(2)

diophantine a^2 + b^2 + c^2 =3(ab + bc + ca)

Source: 2015 VMEO IV Juniors 10.3 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463156_2015_vmeo_iv

9/15/2021
Find all triples of integers (a,b,c)(a, b, c) satisfying a2+b2+c2=3(ab+bc+ca).a^2 + b^2 + c^2 =3(ab + bc + ca).
number theoryDiophantine equationdiophantine
n^m | 5^{n^k} + 1

Source: 2015 VMEO IV Seniors 10.3 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463156_2015_vmeo_iv

9/19/2021
Given a positive integer kk. Find the condition of positive integer mm over kk such that there exists only one positive integer nn satisfying nm∣5nk+1,n^m | 5^{n^k} + 1,
number theorydividesdivisible