Home
Class 10
Maths
Use Euclid's division lemma to show that...

Use Euclid's division lemma to show that the square of any positive integer is either of the form `3m` or `3m+1` for some integer m. [Hint: Let x be any positive integer then it is of the form `3q` , `3q+1` or `3q+2` Now square each of these and sho

Promotional Banner

Similar Questions

Explore conceptually related problems

Use Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

Use Euclids division Lemma to show that the cube of any positive integer is either of the form 9m ,\ 9m+1 or, 9m+8 for some integer m .

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m , 9m+1 or 9m+8 .

Show that the square of any positive integer is of the form 3m or, 3m+1 for some integer m .

Show that the square of any positive integer cannot be of the form 6m+2 or 6m+5 for some integer q.

Show that the square of any positive integer cannot be of the form 5q+2 or 5q+3 for some integer q.

Prove that the square of any positive integer is of the form 4q or 4q+1 for some integer q .

Prove that the square of any positive integer is of the form 4q or 4q+1 for some integer q .

Prove that the square of any positive integer is of the form 5q ,5q+1,5q+4 for some integer q.

Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.