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Show that any positive odd integer of the form 4m+1 or 4m+3 where m is some integer |
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Answer» Step-by-step explanation: Note :- I am taking q as some integer. 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 THANKS #BeBrainly. |
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