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Part of 2019 ISI Entrance Examination

Problems(1)

ISI 2019 : Problem #1

Source: I.S.I. 2019

Prove that the positive integers

n

that cannot be written as a sum of

r

consecutive positive integers, with

r>1

, are of the form

n=2^l~

l\geqslant 0

isiIndian Statistical Institute2019number theory