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Pair (n, p) of nonnegative integers is called nice

Source: Vietnam TST 1995, Problem 5

July 27, 2008

modular arithmeticnumber theory unsolvednumber theory

Problem Statement

For any nonnegative integer

n

, let

f(n)

be the greatest integer such that 2^{f(n)} | n \plus{} 1. A pair

(n, p)

of nonnegative integers is called nice if

2^{f(n)} > p

. Find all triples

(n, p, q)

of nonnegative integers such that the pairs

(n, p)

(p, q)

and (n \plus{} p \plus{} q, n) are all nice.