hi i am new to THIS place here but i do put posts on the number theory site as well. i am in need of direction and have no idea where to turn. i need help w/ two ?'s and they are... how many pos int. <1000 are NOT divisible by 12 or 15? prove the if the sum of two consec. int. is a perfect sq., then the smaller of the two int. is one side of a prim. right. tri. and the large number is the hypot. here's my thoughts so far.... as far as the pos. int. go, could i look at all of the cases of 12 and 15? i mean could i say 15k...15k+14 and then say 12k...12k+11 or would that be too long and drawnout? anyone with a simpler idea? as far as the perfect sq, i know that by consec. int. means i can say this... n is one int. and n+m is the second consec. int. so, i'd have n,n+m. so if the larger ot the two is the hypot. then i can say n + ____ = n+m, right? any one help with these two would be greatly appreciated! also, let me know if i am thinking correctly!! thanks you all!!