self Maths Puzzle

There is one four-digit whole number n, such that the last four digits of n2 are in fact the original number n.

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self Other Question

A popular mathematical pastime:

Use exactly four 4's to form every integer from 0 to 50, using only the operators +, -, x, /, () (brackets) x2 (square), and ! (factorial).
Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)?