Question

11. For some integer m, what is the form of every even integer and odd integer
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Answer 1

Answer:

for even it is 2m And for odd it is 2m+1

Answer 2

1. Question⇒  For some integer m, what is the form of every even integer and odd integer.

Step-by-step explanation:

• We know that, even integers are 2, 4, 6,…
• So, it can be written in the form of 2m.
• where, m = integer = z [since, integer is reprsented by z]
• or m = ...,- 1,0,1,2,3,...
• Alternate method  
• Let 'a' be a positive integer. On dividing 'a' by 2, let m be the quotient and r be the remainder. Then, by Euclid's division algorithm, we have  
• a = 2m + r, where a ≤ r < 2 i.e.,r = 0 and r = 1.
• ⇒ a = 2m or a = 2m + 1
• when, a = 2m for some integer m, then clearly a is even .