Question

show that the square of any positive integer can be of the form 6 m + 2 or 6 m + 5 for any Integer m​

Answer 1

Answer:

Step-by-step explanation:

Let the square of any posititve integer be in the form 6q + 2, 6q +5

x = 6q +2

Squaring both sides

Xsquare = 36(q)square + 4 + 24q

x square = 36(q) square - 6+ 2 + 24q

xsquare = 6 [ 6(q) square - 1 + 4q] + 2

put [ 6(q) square - 1 + 4q] = m

Therefore x = 6m + 2