MathDB

7

Part of 2012 Thailand Mathematical Olympiad

Problems(1)

5 | m - n^2 if gcd (a, b) = 1 and 5 | ma^2 + b^2

Source: Thailand Mathematical Olympiad 2012 p7

8/17/2020
Let a,b,ma, b, m be integers such that gcd (a,b)=1(a, b) = 1 and 5∣ma2+b25 | ma^2 + b^2 . Show that there exists an integer nn such that 5∣m−n25 | m - n^2.
number theorygreatest common divisorGCDdivides