Question

Prove that among 502 positive integers, there are always two integers so that either their sum or their difference is divisible by 1000.

Answer 1

Answer:

We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.

Step-by-step explanation:

We have a 502 positive integers. Therefore we have a numbers 1, 2, 3,.., 500, 501, 502.  

For the sum, we can choose the numbers 502 and 488. We get

(502+488)/1000=1000/1000=1.

For the difference, we can choose the numbers 1 and 501. We get

(1-501)/1000=-500/1000=-0.5.

We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.