help me prove this some plzzz?

Question

if a^2 is divisible by 7 then a is divisble by 7 to

Answer 1

The 'trick' to proving this involves assuming "7 does not divide a" and then showing this leads to a contradiction.

Here's how that goes:

The square of 'a' is divisible by 7 GIVEN
a^2 = 7 * p for whole number 'p' DEFINITION OF DIVISIBILITY
Assume 'a' is not divisible by 7 NEGATION OF CONCLUSION
a^2 = a*a DEFINITION OF SQUARING
a*a = 7p SUBSTITUTION
a*a/7 = p DIVISION
'p' is not a whole number 7 IS NOT A FACTOR OF 'a'
Therefore, 7 MUST divide 'a' PROOF BY CONTRADICTION

There are lots of other ways to accomplish what you sought, although this is my favorite method.

Hope this helps!

Answer 2

See other post for proof!

Please don't repost the same question but read the original posts