6

Part of 1973 Poland - Second Round

Problems(1)

2^m is gcd of a_n = 3^n + w(n)

Source: Polish MO Second Round 1973 p6

Prove that for every non-negative integer

m

there exists a polynomial w with integer coefficients such that

2^m

is the greatest common divisor of the numbers

a_n = 3^n + w(n), n = 0, 1, 2, ....

number theorygreatest common divisor