Shocking Remainder

You may try to search for the answer by using mathematics engine, e.g. wolframaplha.

What's the remainder of division of $23^5$ by $(3^5)^2$ ?

Believe me, it will be quite shocking.

Note: I calculated and find that $23^5 = 2 (\mod 3^6)$ , so I was interested to try finding the largest power of 3 that divides $23^5-2$ . And...

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Xavier Fernandez - 5 years, 9 months ago

It's simply the reason why it's shocking, seriously.

Gian Sanjaya - 5 years, 9 months ago

AH... I forgot, you all may re-share it without permittion

Gian Sanjaya - 5 years, 9 months ago

Can you have a solution to this problem? I mean without mathematics engine.

Renz Gamorot - 5 years, 9 months ago

i just show a fact, not ask you to solv the problem. I just share a hidden fact and the you try to find the fact.

Gian Sanjaya - 5 years, 9 months ago

Yea, my fault. I thought Im solving quizzes here but this was just a share or status somewhat like that. Thanks for answering!

Renz Gamorot - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$