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What is the greatest common divisor of 121^2 + 233^2 + 345^2 and 120^2 + 237^2 + 348^2?

 Oct 25, 2022
 #1
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The gcd is 34.

 Oct 25, 2022
 #2
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What is the greatest common divisor of 121^2 + 233^2 + 345^2 and 120^2 + 237^2 + 348^2?  

 

 

Just checking if the first "Guest" answer is even plausible. 

 

    1212    +    2332    +    3452  

 

= 14,641  +  54,289  +  119,025  

 

=  187,955    This is not evenly divisible by 34 so the first "Guest" is a liar. 

 Oct 25, 2022
 #3
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GCD {[121^2 + 233^2 + 345^2] ,  [120^2 + 237^2 + 348^2]}

 

Prime factorizations


187955 = 5×37591 (2 distinct prime factors)
191673 = 3^3×31×229 (5 prime factors, 3 distinct)

 

Therefore: GCD = 1

 Oct 25, 2022

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