# Ghandhan statement on Characteristic of Fifth power of number $(n \cdot n \cdot n \cdot n \cdot n)$

I have identified few unique characteristics of fifth power of a number i.e. $n \cdot n \cdot n \cdot n \cdot n$. Below are the 2 Characteristics.

## For any integer number N,

1. Last digit of $N$ and its last digit of fifth power $N \cdot N \cdot N \cdot N \cdot N$ are same.
2. Value of $(N\cdot N\cdot N\cdot N \cdot N) - N$ is always divisible by $30$.

Few Examples below,

• $N = 2$,

$$(N\cdot N\cdot N\cdot N \cdot N) = 32$$

$$\left(\frac{(N\cdot N\cdot N\cdot N \cdot N)-N}{30}\right) = 1$$

• $N = 4$

$$(N\cdot N\cdot N\cdot N \cdot N) = 1024$$

$$\left(\frac{(N\cdot N\cdot N\cdot N \cdot N)-N)}{30}\right) = 34$$

If this findings are not valid please defend this statement with your examples.

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What is ghandhan? –  Myself Apr 19 '13 at 9:11