Modulo

Number Theory Level 3

What is the smallest positive integer $b$ such that the following equivalence is satisfied:

$7^{32} \equiv b \pmod {7}$

The answer is 7.

2 solutions

Aditya Raut
Aug 1, 2014

$7^k \equiv 0 \pmod{7}$

Hence the smallest positive value of $b$ is multiple of $7$ , the smallest positive one which is $\boxed{7}$

I wonder how many people originally picked 0 as their answer.

Sharky Kesa - 6 years, 10 months ago

Forgetful "positive" .... we think negative in life most times....

Aditya Raut - 6 years, 10 months ago

What do you think of my modulo set. Good for beginners? :D

Sharky Kesa - 6 years, 10 months ago

@Sharky Kesa – It's awesome. Every prob uses a different concept.

Satvik Golechha - 6 years, 10 months ago

@Satvik Golechha – I had been locked away not making any problems because I was thinking about problems I could make. My patience paid off. Modulo seemed like an awesome topic to do.

Sharky Kesa - 6 years, 10 months ago

@Sharky Kesa – Yeah, you also try my sets... 2 of them are better than others, namely "Mistakes give rise to problems" (this one got famous, and @Satvik Golechha also has posted 1 problem for this set.... ) and other one "vegetable combinatorics".... Not that much for beginners, but good level, some of them are level 4 and 5 problems.

Aditya Raut - 6 years, 10 months ago

@Aditya Raut – In the 'Mistakes give rise to problems', I got all but one right.

Sharky Kesa - 6 years, 10 months ago

Sharky Kesa, I did.

B.S.Bharath Sai Guhan - 6 years, 10 months ago

i was going to write 0 but then i knew that u wouldn't post such an easy question

Adarsh Kumar - 6 years, 10 months ago

In the back of my head I knew the answer was 7, it just seemed a little too dumb to actually be the answer though.

Trevor Arashiro - 6 years, 9 months ago

William Isoroku
Jan 14, 2015

The obvious answer is $0$ but it's not positive. Therefore the smallest positive integer is $7$

Modulo

The answer is 7.

2 solutions

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