Suppose the product of 22 integers is equal to 1. Prove that their sum is not equal to 0.

We select 38 even positive integers, all less than 1000. Prove that there will be two of them whose difference is at most 26.   Please explain it correct.

prove the following using either direct or indirect proof  a. if a is an odd integer, then 5a^2-3a+5 is odd   b. if x+y is greater or equal to 2, then x is greater or equal to 1 or y is greater or equal to 1

If a and b are odd positive integers, and the sum of the integers, less than a and greater than b, is 1000; then find a and b.