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    Proofs : GCDs and Primes

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    1. (i) Find the gcd (210, 48) using factorizations into primes
    (ii)Find (1234, 5678)

    2. Prove that there are no integers x, y, and z such that
    x^2 + y^2 + z^2 = 999

    keywords: greatest comon divisor

    © BrainMass Inc. brainmass.com October 9, 2019, 6:45 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/proofs-gcds-and-primes-97074

    Solution Preview

    Problem #1
    (i) We use factorizations.
    210 = 2*3*5*7
    48 = 2*2*2*2*3
    Thus gcd(210,48)=2*3=6
    (2) To find gcd(1234,5678), we can use the Eucliean algorithm.
    5678 = 4*1234 + 742
    1234 = 1*742 + 492
    742 = 1*492 + ...

    Solution Summary

    Proofs involving GCDs and Primes are provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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