If n is an odd integer, then show that n2 – 1 is divisible by 8.
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Show that any positive odd integer is of the form 6q+1,6q+3 & 6q+5 where q is some integer.
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,...
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Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
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 = 0,1,2,3,4,5 because 0 ≤ r ≤ 6. So, a...
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Show that the square of any odd integer is of the form 4q + 1, for some integer q.
Solution: 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 <...
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If n is an odd integer, then show that n^2 – 1 is divisible by 8.
Y are you taking some odd integers as 4m+1 or 4m+3. Why no we take 2m+1 or 3m+1
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If n is an odd integer, then show that n^2 – 1 is divisible by 8.
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If n is an odd integer, then show that n^2 – 1 is divisible by 8.
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n^2 - 1 is divisible by 8, if n is (A) an integer (B) a natural number (C) an odd integer (D) an even integer
n2 - 1 is divisible by 8, if n is an odd integer
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Show that the square of an odd positive integer is of the form 8q + 1, for some integer q.
By Euclid’s division algorithm a = bq + r, where 0 ≤ r ≤ b Put b = 4 a = 4q + r, where 0 ≤ r ≤ 4 If r = 0,...
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If n is an odd positive integer, show that (n^2-1) divisible by 8.
Because every odd integer will cover by 4m+1 or 4m+3. You may also use 2m+1.
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Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer
Let 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...
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