show that any positive odd integer is of the form (4m+1) or (4m+3) where m is some integer.

show that any positive odd integer is of the form (4m+1) or (4m+3) whe

1.	show that any positive odd integer is of the form (4m+1) or (4m+3) where m is some integer.
Answer» 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 = 2a = 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\xa0