1.

Show that any positive odd integer of the form 4m+1 or 4m+3 where m is some integer

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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