Modular Arithmetic

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Modular Arithmetic

Postby ZekeusAurelius » Fri Apr 19, 2013 4:31 pm

Could someone explain this one to me? I'm sure it has something to do with modulus.
Two integers multiply to 17836. Both are divisible by 7, and the smaller number is divisible by 4 as well. What is the sum of the two integers?
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Re: Modular Arithmetic

Postby Fredfredburger » Fri Apr 19, 2013 9:34 pm

Here's my solution, don't use mods though

The square root of 17836 is 135.55..., so the smaller factor is less than 135. The other factor is also in the form 4*7*k or 28k where k is a positive integer, because 4 and 7 are relatively prime. That means you have to only test the numbers 28, 56, 84 and 112.

The only number that even divides is 28, and the quotient is 637, which is divisble by 7. 637+28=665
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Re: Modular Arithmetic

Postby sxk1693 » Sat Apr 20, 2013 10:21 pm

Way to complicated. Just factor the numbers(in 89) and satisfy the constraints.
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Re: Modular Arithmetic

Postby ZekeusAurelius » Mon Apr 22, 2013 1:15 pm

Sweet I like that solution, I feel dumb for not figuring that out before
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