SOLUTION: If remainder of (5m+1)(5m+3)(5m+4)/5 is a natural number then find the remainder.

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Question 288613: If remainder of (5m+1)(5m+3)(5m+4)/5 is a natural number then find the remainder.
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
if m=0 then 12/5=2 +2/5
remainder 2
if m=1 6*8*9/5=86 2/5
remainder 2

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

%28%285m%2B1%29%285m%2B3%29%285m%2B4%29%29%2F5

%28%2825m%5E2%2B20m%2B3%29%285m%2B4%29%29%2F5

%28125m%5E3%2B100m%5E2%2B100m%5E2%2B80m%2B15m%2B12%29%2F5

%28125m%5E3%2B200m%5E2%2B95m%2B12%29%2F5

25m%5E3%2F5%2B200m%5E2%2F5%2B95m%2F5%2B12%2F5

5m%5E3%2B40m%5E2%2B19m%2B12%2F5

Write the 12 as 10+2

5m%5E3%2B40m%5E2%2B19m%2B%2810%2B2%29%2F5

5m%5E3%2B40m%5E2%2B19m%2B10%2F5%2B2%2F5

5m%5E3%2B40m%5E2%2B19m%2B2%2B2%2F5

So the fraction part when dividing by 5 was 2%2F5 so the

remainder had to be 2

Edwin