The sum of 2 consecutive odd integers is always a multiple of 4. Providing proof, is the statement true or false?

2 Answers
Jul 23, 2018

This statement is true

Explanation:

Let #m# and #n# be two consecutive odd integers:
Sums of #m# and #n#
#3+5=8#
#5+7=12#
#7+9=16#
#(-1)+(-3)=-4#

This statement is true

I used inductive reasoning, for a proof with deductive reasoning, refer to the answer above

Jul 24, 2018

True

Explanation:

Consider: #(2n-1)# for any #n in ZZ# is an odd integer.

The next consecutive odd integer will be: #(2n+1)#

Sum #= (2n-1) + (2n+1) = 4n#

Hence, the sum of any two consecutive odd integers will be a multiple of 4.