Prove that discrete math: 1)If a|b and a|c then a|(b^2

iohanetc

iohanetc

Answered question

2021-08-14

Prove that discrete math:

1) If a|b and a|c then a|(b24c)
2) If a|b then a2|b2

Answer & Explanation

Alara Mccarthy

Alara Mccarthy

Skilled2021-08-15Added 85 answers

If a and b are integers then from a/b it can said that b=am where m is an integer.
Assume a,b and c are integers.
Assume m is also an integer.
So, from a/b it is concluded that,
b=am …..(1)
Assume n is also an integer.
So, from a/c it is concluded that,
c=an …..(2)
Multiply equation (1) by b and equation (2) by 4.
So,
(b)(b)=(b)(am)
b2=a(mb)...(3)
(4)c=(4)an
4c=a(4n)..(4)
subtract equation (4) from equation (3). b24c=a(mb)a(4n)
=a(mb4n)
As m , b, 4 and c are integers. So, mb-4n will also be integer.
Thus, we can write
ab24c

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