If x is odd, then x+1 is even. Try this out with a few numbers.
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They are 391 plus 392 = 783
x+3 and x+4 would be consecutive integers.
If x is even, then x+1 is odd. Try this out with a few numbers, to get a "feel" for the situation.
No. The sum of four consecutive integers is two odd numbers plus two even numbers which is an even number. 2001 is an odd number, therefore it cannot be the sum of four consecutive numbers.
10+(X)+(X+1)=196 10+2X+1=196 11+2X=196 2X=185 X=92.5 Therefore, ten plus the sum of two consecutive integers can not be even.