show that every positive odd integer is of form 4q+1or4q where q is some integer
Attachments:
Answers
Answered by
0
because if we multiply every odd positive integer with even number it becomes even and if we add odd integer it becomes odd
hope it helps you
hope it helps you
Answered by
4
Step-by-step explanation:
Let a be the positive integer.
And, b = 4 .
Then by Euclid's division lemma,
We can write a = 4q + r ,for some integer q and 0 ≤ r < 4 .
°•° Then, possible values of r is 0, 1, 2, 3 .
Taking r = 0 .
a = 4q .
Taking r = 1 .
a = 4q + 1 .
Taking r = 2
a = 4q + 2 .
Taking r = 3 .
a = 4q + 3 .
But a is an odd positive integer, so a can't be 4q , or 4q + 2 [ As these are even ] .
•°• a can be of the form 4q + 1 or 4q + 3 for some integer q .
Hence , it is solved .
Similar questions