Parity of Sum

Number Theory Level 2

If all the numbers ( a 1 + a 2 ) (a_1+a_2) , ( a 2 + a 3 ) , … , ( a n − 1 + a n ) (a_2+a_3), \ldots, (a_{n-1}+a_n) are odd, then what is the parity of n ( a n + a 1 ) n(a_n+a_1) ?

Assumption :

  • Each of a i a_i (s) and n n is integer.
Can be of different parity depending on the parity of n n Can be of different parity depending on the choice of values for a i a_i (s) Odd Even

Muhammad Rasel Parvej by Muhammad Rasel Parvej , 27, Bangladesh

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1 solution

Ma Pm
Dec 21, 2016

n always must be even. Every binomy takes two númbers. (A1+An) is odd or even. n (A1+An) is even.

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Wrong Proof!

Muhammad Rasel Parvej - 4 years, 5 months ago

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