Show that the square of an odd positive integer is of the form 8m + 1, for some integer m
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We can substitute any odd positive integer for the answer.
3² = 9 where m=1 & (8 x 1) + 1 = 8+1 = 9
5² = 25 where m = 2 & (8 x 3) + 1 = 24 +1 = 25
3² = 9 where m=1 & (8 x 1) + 1 = 8+1 = 9
5² = 25 where m = 2 & (8 x 3) + 1 = 24 +1 = 25
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Answered by
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Let us take a variable q ,where q us a positive odd integer.
We apply the division algorithm:
0 lesser than or =to r lesser than 8
the possible zeroes are 0,1,2,3.
a=4m+1
(squaring on both sides)
a2=(4m+1)2
a2=16m2 +1
=8(2m square )+1
(where 2m square =m)
=8m+1
Hope this helps uh !!!
We apply the division algorithm:
0 lesser than or =to r lesser than 8
the possible zeroes are 0,1,2,3.
a=4m+1
(squaring on both sides)
a2=(4m+1)2
a2=16m2 +1
=8(2m square )+1
(where 2m square =m)
=8m+1
Hope this helps uh !!!
thanks
wlcm
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