Modulo - rekning

[Mattebruker]

Rekn ut 10^42 mod 61

Hint: 42 = 2 + 8 + 32

[MaximilliaVeum]

Hello Mattebruker. Your question is quite complex. I hope this helps:
61=308−(61×5)=308−305=3
308mod61=308−(61×5)=308−305=3
....

[Mattebruker]

Hello !

I don't realize where the number ( 308 ) comes from. You should rather take into account the hint given in text ( 42 = 2 + 8 + 32 ).
Maybe this rewriting will lead you onto a more fruitful trace:

10^42 = 10^2 * 10^8 * 10^32

Another hint: 10^2 = 100 " KONGRUENT " 39 ( MOD 61 )

10^4 = ( 10^2 )^ 2 " KONGRUENT " 39^2 = ( 40 - 1 )^2 = 40^2 - 2 * 40 * 1 + 1 = 1521 = 1525 - 4 = ( 61 * 25 - 4) " kongruent " -4 ( mod 61 )

Do you see how to move forward ? Good luck !

[salimnl]

Hello !
Incredibox
I don't realize where the number ( 308 ) comes from. You should rather take into account the hint given in text ( 42 = 2 + 8 + 32 ).
Maybe this rewriting will lead you onto a more fruitful trace:

10^42 = 10^2 * 10^8 * 10^32

Another hint: 10^2 = 100 " KONGRUENT " 39 ( MOD 61 )

10^4 = ( 10^2 )^ 2 " KONGRUENT " 39^2 = ( 40 - 1 )^2 = 40^2 - 2 * 40 * 1 + 1 = 1521 = 1525 - 4 = ( 61 * 25 - 4) " kongruent " -4 ( mod 61 )

Do you see how to move forward ? Good luck !

I have a small question, could you explain more about how "kongruent" is applied in this problem? It feels like there is a special connection between the operations and I would like to understand this method more deeply.

[GloriaRoth]

Hello !

I don't realize where the number ( 308 ) comes from. You should rather take into account the hint given in text ( 42 = 2 + 8 + 32 ).
Maybe this rewriting will lead you onto a more fruitful trace:

10^42 = 10^2 * 10^8 * 10^32

Another hint: 10^2 = 100 " KONGRUENT " 39 ( MOD 61 )

10^4 = ( 10^2 )^ 2 " KONGRUENT " 39^2 = ( 40 - 1 )^2 = 40^2 - 2 * 40 * 1 + 1 = 1521 = 1525 - 4 = ( 61 * 25 - 4) " kongruent " -4 ( mod 61 )

Do you see how to move forward ? Good luck !

I have a small question, could you explain more about how "kongruent Geometry Dash" is applied in this problem? It feels like there is a special connection between the operations and I would like to understand this method more deeply.

In mathematics, saying two numbers are kongruent (or congruent in English) modulo n means:
a ≡ b (modn)
This means that a and b leave the same remainder when divided by n, or equivalently, n divides (a - b).

[otis5842]

Hello !
Stickman Hook
I don't realize where the number ( 308 ) comes from. You should rather take into account the hint given in text ( 42 = 2 + 8 + 32 ).
Maybe this rewriting will lead you onto a more fruitful trace:

10^42 = 10^2 * 10^8 * 10^32

Another hint: 10^2 = 100 " KONGRUENT " 39 ( MOD 61 )

10^4 = ( 10^2 )^ 2 " KONGRUENT " 39^2 = ( 40 - 1 )^2 = 40^2 - 2 * 40 * 1 + 1 = 1521 = 1525 - 4 = ( 61 * 25 - 4) " kongruent " -4 ( mod 61 )

Do you see how to move forward ? Good luck !

I have a small question, could you explain more about how "kongruent" is applied in this problem? It feels like there is a special connection between the operations and I would like to understand this method more deeply.

Interestingly, 308 appeared in our calculation (
14
⋅
22
=
308
14⋅22=308) before reducing modulo 61 to get 3. This might explain your mention of 308—it’s a partial result before the final reduction. If you meant something else by 308, please provide more context, and I’ll investigate!