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Find all rationals s.t..

Source: Indian RMO 1994 Problem 7

October 25, 2005

number theoryrelatively prime

Problem Statement

Find the number of rationals

\frac{m}{n}

such that
(i)

0 < \frac{m}{n} < 1

;
(ii)

m

and

n

are relatively prime;
(iii)

mn = 25!

.

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