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Source: Chinese MO 1999

October 12, 2005

modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let

m

be a positive integer. Prove that there are integers

a, b, k

, such that both

a

and

b

are odd,

k\geq0

and

2m=a^{19}+b^{99}+k\cdot2^{1999}