About Use the given equations in a complete proof of each theorem. Your proof should be expressed in complete English sentences. (a) Theorem: If a, b, and c are integers such that a3|b and b2|c, then a6|c.

(b) Theorem: If m and n are integers such that m|n, then m|(5n3 - 2n2 3n).

(c) Theorem: If n is an odd integer, then 4 divides n2-1.

(d) Theorem:The sum of the squares of any two consecutive integers is odd.

step-by-step explanation:

try remembering the steps

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

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step-by-step explanation:

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