If we divide the number 13 by the three numbers 5,7, and 9, then these divisions leave remainders: when dividing by 5 the remainder is 3, when dividing by 7 the remainder is 6, and when dividing by 9 the remainder is 4. If we add these remainders, we obtain 3+6+4=13, the original number.
(a) Let n be a positive integer and let a and b be two positive integers smaller than n. Prove: if you divide n by a and b, then the sum of the two remainders never equals n.
(b) Determine all integers n>229 having the property that if you divide n by 99,132, and 229, the sum of the three remainders is n. remainderSumnumber theory