MathDB

4

Part of 2011 Dutch BxMO TST

Problems(1)

a,b greatest pos. integer such 2^a | (5^n - 3^n), 2^b <= n, prove a<=b+3

Source: Dutch BxMO TST 2011 p4

8/24/2019
Let n≥2n \ge 2 be an integer. Let aa be the greatest positive integer such that 2a∣5n−3n2^a | 5^n - 3^n. Let bb be the greatest positive integer such that 2b≤n2^b \le n. Prove that a≤b+3a \le b + 3.
number theoryinequalitiesalgebra