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An Integer Product (Posted on 2022-05-26) Difficulty: 3 of 5
P(n) is defined as an n-term product (4-2/1)*(4-2/2)*...*(4-2/n).

Prove P(n) is an integer for all natural numbers n.

See The Solution Submitted by Brian Smith    
Rating: 5.0000 (1 votes)

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re(2): demonstration | Comment 4 of 7 |
(In reply to re: demonstration by Kenny M)

In the numerator the prime just multiplies the other factors that make an integer by another integer (the prime).


Any problems toward being integral would come from the denominator, but that doesn't happen as any number prime or otherwise in the denominator is present twice in both the numerator and denominator. As said above, other primes in the numerator are themselves integral and being in the numerator just multiply one integer by another.

Edited on May 26, 2022, 5:37 pm
  Posted by Charlie on 2022-05-26 17:28:51

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