# URGENT help needed with maths question ?

A positive integer ends in the digit 4 and has the property that it becomes four times as large when the 4 is moved from the end and placed at the front. what is the smallest such number?

Does anyone know how to solve this with good working?

Thanks

### 2 Answers

- ToddLv 72 months ago
You're going to have to prove there is no such number. This will not be easy to do, but it probably has something to do with the fact the first grows arithmetically by 10 (4, 14, 24, 34...), the second geometrically by 4 (4*4, 14*4, , 24*4...). But that is definitely not sufficient to definitively show the number doesn't exist. It might be something weird like numbers that have the quality of being indivisible by 5 when offset by 4 in the arithmetic series, whereas in the geometric series, the numbers must always be divisible by 4 by definition. Another way to put it is that any number ending in 4, when multiplied by 4 cannot also be divisible by a number divisible by 10 with 4 added to it (number y modded by 10 is 4).

- KrishnamurthyLv 72 months ago
A positive integer ends in the digit 4 and has the property that it becomes four times as large when the 4 is moved from the end and placed at the front.

What is the smallest such number?

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Thank you