SOLUTION: Show that the sum of two consecutive numbers is not even.

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Question 984747: Show that the sum of two consecutive numbers is not even.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be any integer.
x and x+1 are consecutive integers, x%2B1%3Ex.

Either must be odd and the other must be even.

x+(x+1) is either ODD + EVEN or it is EVEN + ODD;

ODD+EVEN is ODD; and EVEN+ODD is ODD.
Neither arrangement is even.

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Maybe a better way.
x%2B%28x%2B1%29, the sum of the consecutive numbers;
x%2Bx%2B1
2x%2B1
The summand 2x is EVEN. It is multiple of 2 and an integer, the factor 2 ensuring 2x be even. 2x%2B1, ODD; %282x%2B1%29%2F2 NOT an element of the Integers. EVEN and ODD numbers are always Integers.