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There is a whole number n for which the following holds: if you put a 4 at the end of n, and multiply the number you get in that way by 4, the result is equal to the number you get if you put a 4 in front of n. In other words, we are looking for the number you can put on the dots in the following equation: 4... = 4 ?...4 Which number must be put on the dots to get a correct equation?

Answer:

n4*4=4n.
1) if n is single digit number then we get n will be fraction.
2)similarly tru for n as 2,3,4 digit numbers we won't get.
3) let n=abcde
then
abcde4*4=4abcde

which by solving we get 13*abcde=133328
so abcde=10256.

thus 102564*4=410256

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