If n is an odd integer, then show that n2 – 1 is divisible by 8.
Solution: Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0, and r = 0, 1, 2, 3,...
1 Answers 1 viewsSolution: Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0 and r = 0,1,2,3,4,5 because 0 ≤ r ≤ 6. So, a...
1 Answers 1 viewsSolution: Let a be any odd integer and b = 4. Then, by Euclid’s algorithm, a = 4m + r for some integer m ≥ 0 and r = 0,1,2,3 because 0 ≤ r <...
1 Answers 1 viewsY are you taking some odd integers as 4m+1 or 4m+3. Why no we take 2m+1 or 3m+1
1 Answers 1 viewsn2 - 1 is divisible by 8, if n is an odd integer
1 Answers 1 viewsBy Euclid’s division algorithm a = bq + r, where 0 ≤ r ≤ b Put b = 4 a = 4q + r, where 0 ≤ r ≤ 4 If r = 0,...
1 Answers 1 viewsBecause every odd integer will cover by 4m+1 or 4m+3. You may also use 2m+1.
1 Answers 1 viewsLet a be any positive odd integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0 and 0 ≤ r...
1 Answers 1 views