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2
exist a,b among 43 pos. integers 100 divides a^2-b^2 (2019 Auckland MO S2)
exist a,b among 43 pos. integers 100 divides a^2-b^2 (2019 Auckland MO S2)
Source:
November 15, 2021
number theory
divisible
divides
Problem Statement
Prove that among any
43
43
43
positive integers there exist two
a
a
a
and
b
b
b
such that
a
2
ā
b
2
a^2 - b^2
a
2
ā
b
2
is divisible by
100
100
100
.
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