If you have two sets of integers {1, 2, 3, 4} and {4, 5, 6, 7}, then the sum of each set is 10 and 22, respectively, with a difference of 12. Based on logic, we know that this applies to any numbers you choose that meet the criteria. Number theory offers a more formalized outlook on these concepts.
Try this explanation, using algebra principles: 1) let the 1st set consists of integers: x; x+1; x+2; x+3, then, according to the condition, the 2d set consists of integers: x+3;x+4;x+5;x+6. Note, in this case 'x+3' is common integer. 2) The sum of 2d set is (x+3)+(x+4)+(x+5)+(x+6)=4x+18; the sum of the 1st set is x+(x+1)+(x+2)+(x+3)=4x+6. The difference between the set with greater number and the another set is: (4x+18)-(4x+6)=12. PS. the same result is, when 'x' is common integer.
