Congruence makes my day

a a a . . . . m times 0 m o d ( am ) {a^{a^{a^{....^{\text{m times}}}}} \equiv 0 \mod (\text{am})}

for all prime a’s \text{a's}

The congruence above is __________ \text{\_\_\_\_\_\_\_\_\_\_} .

True False

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1 solution

Otto Bretscher
Mar 19, 2016

Let a = 2 a=2 and m = 3 m=3 . Then 2 2 2 2^{2^2} fails to be divisible by 6.

LOL yes :))

A Former Brilliant Member - 5 years, 2 months ago

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You can define the hyperoperation as Tetration operator. so

n a = a a a m times \large { ^{ n }a }=\underbrace { { a }^{ { a }^{ { \dots }^{ a } } } }_{ m \text{ times} }

Arulx Z - 5 years, 2 months ago

can you plz tell that from where have you studied modular arithmetic ,you go in some coaching institute

Deepansh Jindal - 5 years, 2 months ago

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I do not go to any coaching institute , I have studied it on my own ....

For basics you may see Brilliant Wikis .... then for little higher NT you may see Elementary NT by Burton,....

A Former Brilliant Member - 5 years, 2 months ago

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@A Former Brilliant Member have you appeared in tallentex ,Olympiads by hbcse RMO and NMTC ,if appeared what were your ranks in those exam ,,please tell

Deepansh Jindal - 5 years, 2 months ago

J'ai choisi a=5, m=10k. Cela a rendu facile

Department 8 - 5 years, 2 months ago

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You have a counterexample whenever m m isn't a power of a a .

Otto Bretscher - 5 years, 2 months ago

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Oui! Belle observation

Department 8 - 5 years, 2 months ago

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@Department 8 That's german?

Kushagra Sahni - 5 years, 2 months ago

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@Kushagra Sahni No i think its French

A Former Brilliant Member - 5 years, 2 months ago

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@A Former Brilliant Member Yes,that's French.

Rohit Udaiwal - 5 years, 2 months ago

@Kushagra Sahni Mais oui, c'est français, nicht Deutsch ;)

Otto Bretscher - 5 years, 2 months ago

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@Otto Bretscher All right.

Kushagra Sahni - 5 years, 2 months ago

Google Translate jedermann?

Arulx Z - 5 years, 2 months ago

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J'étudie la langue français à l'école

Department 8 - 5 years, 2 months ago

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@Department 8 Magnifique! La langue de la philosophie, les mathématiques ... et de l'amour! ;)

Otto Bretscher - 5 years, 2 months ago

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@Otto Bretscher How many languages do you know comrade !!! @Otto Bretscher

A Former Brilliant Member - 5 years, 2 months ago

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@A Former Brilliant Member Indians also know atleast 3, Hindi English and the language of their ethnic community like Punjabi in my case.

Kushagra Sahni - 5 years, 2 months ago

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