Problem Solving (PS) | Re: If P = m^3 - m, where m and P are positive integers, and m is given by

Realise that 10x^n will be just some number ending in 1...00 for x>=2 or 10 for x=1.

For the case of x=1, the last two digits of the 3 expanded numbers of p become
(25+10-1)(25+10)(25+10+1)
(34)(35)(36)
36 is divisble by 4, so all of P is divisible by 4.

No need to do the case of x>=2, but in this case the last two digits become:
(24)(25)(26), which have enough 2s to be divided by 4.

E.

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Statistics : Posted by mysterymanrog • on 24 Jan 2022, 09:15 • Replies 3 • Views 1360

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