A number theory problem by Trung Le

Number Theory Level 3

Is it always true that if gcd ⁡ ( a , b ) = m , \gcd(a, b) = m, and gcd ⁡ ( c , d ) = n , \gcd(c, d) = n, then gcd ⁡ ( a c , b d ) = m n ? \gcd(ac, bd) = mn?

Yes No

Trung Le by Trung Le , 58, Vietnam

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1 solution

Trung Le
Nov 11, 2015

Below is a counter-example: gcd(3, 9) = 3, gcd(9, 3) = 3, gcd(3x9, 9x3) = gcd(27, 27) = 27, which is not 3x3 = 9

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