Prove or disprove: If a, b, c are any three distinct positive integers such that 1/a...

Prove or disprove:

If a, b, c are any three distinct positive integers such that 1/a + 1/b + 1/c = 1, then a + b + c is a prime.

Solutions

Expert Solution

we will prove this result:

Thus, we have proved that a+b+c is always prime.
Had the condition of distinctness be removed, we would have gotten more solutions which would have disproved this result (3,3,3)

If doubts bug you, feel free to comment your query!

Colby Messinger answered 1 year ago

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