+45 The remainders when three positive integers are divided by 5 are 1, 2, and 3. Find the remainder when their product is divided by 5.
+128517 Let the integers be
5m + 1 , 5n + 2 and 5p + 3
Their product = ( 5m + 1) ( 5n + 2) ( 5p + 3) =
(25mn + 5n + 10m + 2) ( 5p + 3) =
125 pmn + 25pn + 50pm + 10p + 75mn + 15n + 30m + 6
Each of the first terms divided by 5 will yield and integer and these added together will also yield an integer
Only the last term divided by 5 will yield a remainder of 1
