Question

1) Show that the square of an odd positive integer is of the form 8q+1, for some integer q.
2) Prove that the square of any positive integer of the form 5q+1 is of the same form.
3) A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10ft by 8ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?
4) Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by 8,15 and 21.
PLEASE GIVE EXPLANATION FOR ALL QUESTIONS.

Answer 1

Sol1:The square of an odd positive integer in the form of 8q+1 : 4q+1