A number AABB is the square of an integer. Find this integer, aided by pen and paper. No other calculating aids allowed.
From the pattern, div by 11
AABB = 11 * A0B
A0B also div by 11 so A+B=11
(A,B cannot be 0 or 1)
but A0B/11 must be a square.
Squares only end in 1,4,9,6,5,0
Multiplying a square by 11 does not change the last digit.
B could be {4,5,6,9}
A could be {7,6,5,2}
A0B can only be {209,506,605,704)
Dividing these by 11:
{19,46,55,64}
64 is the only square;
AABB = 7744 = 11*11*8*8 = 8^2
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Posted by Larry
on 2024-10-01 15:48:35 |
my answer
