A Pythagorean triple is a set of positive integers a<b<c such that a2+b2=c2. Some examples are
32+4252+12282+152=52=132=172.
Note that each of these Pythagorean triples contains a multiple of 5.
How many Pythagorean triples {a,b,c} are there for which none of the three numbers is a multiple of 5 and c≤1000?