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Solve equation with least prime divisors

Source: 2008 Peru Iberoamerican TST Problem 1

May 8, 2023

number theory

Problem Statement

For every integer

m>1

, let

p(m)

be the least prime divisor of

m

. If

a

and

b

are integers greater than

1

such that:

a^2+b=p(a)+[p(b)]^2

Show that

a=b

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