Proving/Disproving: Coprimes & (an + bn + cn ) / abc

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SUMMARY

The discussion centers on the mathematical property of coprime integers a, b, and c, specifically regarding the expression (an + bn + cn) / abc. It is established that if a, b, and c are coprime, then the result of this expression cannot yield an integer unless the sum an + bn + cn is divisible by abc. The example provided, 23 + 33 + 73, serves to illustrate this property, prompting further exploration of its implications.

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  • Understanding of coprime integers
  • Familiarity with integer divisibility
  • Basic knowledge of algebraic expressions
  • Concept of modular arithmetic
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  • Research the properties of coprime integers in number theory
  • Explore integer divisibility rules and their applications
  • Study algebraic expressions and their simplifications
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Mathematicians, students studying number theory, and anyone interested in the properties of coprime integers and their applications in algebra.

mahmudarif
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if a, b, c (integers) are coprimes then (an + bn + cn ) / abc can't be a number that is not a fraction (integer). Any idea to prove/disprove it will be highly appreciated.
 
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If the sum is divisibleby abc what does that say about the terms
 
23+33+73
 

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