1.show that every positive integer is of the form of 3q,3q+1,and 3q+2
2.st every positive integer is of form 2q and that of every postive odd integer is 2q+1
3.st every postive integer is of form 4q+1,4q+3 for some odd positive integrr
4.st square of any postive einteger in the form of 3m,3m+1 where m is some int
5.st cube of any int is of form 9m,9m+1,9m+8
6.pt one of every 3 consecutive integers is divisble by 3.(n-1,n,n+1)
7.pt product of any two consecutive int is divisble by2
8.pt product of 3 consecutive int is div by 6
9.for any positive int n,pt n3 - n ( n3 means n cube) is div by 6
10..pt square of any positive int is if the form 4q,4q+1
11..pt square of any positive int is of form 5q 5q+1 , 5q+4
12.pt sq of any odd posotive int is of form 8q+1
13.st n2- 1(n square minus 1) is divisble by 8.if n is odd positive int
14.pt n2-n (n sqiare minus n) is divisble by 2.for every positive int
15.st every odd positive int is if the form 6q+1,6q+3,6q+5
16.st square of any positive int cannot be of form 6m+2,6m+5
17.st one and only one out of n,n+4,n+8,n+12,n+16 is divible by 5
18.st square of odd positiv int can be of form 6q+1,6q+3 for any positiv int
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