Perfect
Square
Any perfect square
satisfies the following three properties:
·
The possible ones of perfect square
number is either 0, 1, 4, 5, 6, dan 9.
·
If 4
divides a perfect square then the remainder is either 0 or 1.
·
If p
is a prime and p | x2 then
p|z , where z = x2 = p.
Example :
Obtain a perfect square
whose digits are k; k + 1; k + 2; 3k; k +
3.
Solution. The ones of
the number is k +3, it follows that k can be either 1; 2; 3 or
6.
Whilst
the tens is 3k, it follows that k can
be either 0; 1; 2 or 3. They imply
that
the possible k is
either 1; 2 or 3 which give perfect
square numbers 12334; 23465
or 34596. Since the remainder of
12334 divided by 4 is 2, it gives that 12334 is
not a perfect square.
The remainder of 23465 divided by 4 is
1 and 5|23465, but
5†
4693, so that 23465 is
not a perfect square. Now, 4|34596, and we have the
Following
2 | 34596
2 | 17298
3 | 8649
3 | 2883
31
| 961
31
| 31
Therefore, 34596 = 22.32.312=186 which is a perfect square.
