Originally posted by David113
True or false:
If n is an integer, and n squared minus 5 is divisible by an integer m, then the last digit of m cannot be 3 or 7.
for it to work, the last digit of the squared number (after being squared) would have to be a 2 or an 8
meaning that n must be even (even number times even number equals even number and viceversa for odd numbers)when two numbers are squared, the last digit of the product is determined by the last digit of n, which must be 2 4 6 8 or 0
these squares are 4, 16, 36, 64, and 0
since we are concerned about the last digit of these numbers, we can isolate them as:
4, 6, 6, 4, and 0
meaning that the square of any number will never have a 2 or 8 as its last digit...
so the last digit of m will never be 3 or 7 after subtracting 5...