Question

Prove that the square of an odd number is always 1 more than a multiple of 4

Answer 1

Answer:

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Step-by-step explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

${3}^{2} = 9$

8 is a multiple of 4, and 9 is more than 8.

${11}^{2} = 121$

120 is a multiple of 4 and 121 is one more than it.

${25}^{2} = 625$

624 is a multiple of 4 and 625 is one more than it.

${37}^{2} = 1369$

1368 is a multiple of 4 and 1369 is one more than 1368.

${131}^{2} = 17161$

17160 is a multiple of 4.