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Maximum number of perfect squares

Source: AllRussian-2014, Grade 9, day1, P2

May 3, 2014

number theorynumber theory proposed

Problem Statement

Sergei chooses two different natural numbers

a

and

b

. He writes four numbers in a notebook:

a

a+2

b

and

b+2

. He then writes all six pairwise products of the numbers of notebook on the blackboard. Let

S

be the number of perfect squares on the blackboard. Find the maximum value of

S

.
S. Berlov