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TOT 1998 Autumn AJ1 AS1 lcm (a, b) = lcm (a + c, b + c)

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May 11, 2020

number theoryleast common multipleLCM

Problem Statement

(a) Prove that for any two positive integers a and b the equation

lcm (a, a + 5) = lcm (b, b + 5)

implies

a = b

. (b) Is it possible that

lcm (a, b) = lcm (a + c, b + c)

for positive integers

a, b

and

c

?
(A Shapovalov)
PS. part (a) for Juniors, both part for Seniors