perplexus.info :: Just Math : A reducible expression

A reducible expression (Posted on 2024-11-17)

Compute the smallest positive integer k such that the fraction (7k+100)/(5k-3) is reducible.

No Solution Yet Submitted by Danish Ahmed Khan

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brute force

| Comment 2 of 3 |

for k=1:1000

n=7*k+100;

d=5*k-3;

if gcd(n,d)>1

disp([k,n,d,gcd(n,d)])

end

    k       numerator   denminator     GCD
   209        1563        1042         521
   730        5210        3647         521

The smallest k is 209.

Posted by Charlie on 2024-11-17 13:06:14

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