# mod

1. ### Simplify modulus expression

Can someone tell me how to simplify this expression with modulus: (A/100) mod 10 + (A/10) mod 10 + A mod 10 where A is an integer, but it can also be not divisible by 100. I tried doing this, but it doesn't work... (A/100+A/10+A)mod 10 Thanks
2. ### arithmetics

Hello, I am a student in discrete mathematics and I have trouble solving this problem. Any help track is welcome! Here is the problem: A boat sinks in the ocean and the 5 survivors each jump in a different lifeboat. They meet on the deserted island in the distance. The next morning, the first...
3. ### Solve x^120 + x^3 + 2x^2 + x +3 â‰¡ 0 (mod 7)

Hi, I'm having trouble with this one: x^120 + x^3 + 2x^2 + x +3 â‰¡ 0 (mod 7) What is x?
4. ### super huge numbers mod a big number

what is the general method for say finding the last 10 digits of the number $n=2012^{2011^{2010}}$ I'm thinking that you first find $n_1=2012^{2011}\pmod{10^{10}}$ and then $n_2 = n_1^{2010} \pmod{10^{10}}$ and if say $10^{10}$ was prime, or relatively prime to $2012$ then...
5. ### Mod functions related to Fermat's Last Theorem

Since Fermat's Last Theorem has been proved, can it be concluded that there can't be three different, relatively prime, non zero integers A>B>C where the following six Mod functions are all equal to zero when the power is odd and higher than one and all but the first Mod function are equal to...
6. ### f(n)=-1 mod p has a solution iff a condition on p

Hello Can you please share with me all the results that you know like this: f(n)=-1 mod p has a solution iff a condition on p example : Lagrange Lemma: x^2=-1 mod p has a solution if and only if p=1 mod 4 1) Is this kind of equation important? 2) I wish that you share with me any book...
7. ### limit of Mod functions

lim |x|/x as x->infinity I Think this should be = 1 as this is indeterminate form and we can apply L Hospitals Rule . But the text book answer says that limit does not exist . which one is correct
8. ### Mod Opertaor

I don't understand this question - Please help me understand why it is true or false. If a â‰¡ x1 (mod m) and b â‰¡ y1 (mod m), then we will have ab â‰¡ x1y1 (mod m). True or False and why? Thank you.
9. ### Congruence 3x â‰¡ 2 (mod 7). Find all $x \in Z$

Hi, I have to find all $x \in \mathbb{Z}$ that satisfy the following congruence: $3x \equiv 2 \mbox{ (mod 7) }$ I think that for search every x I have to go by attempts, and I think that there isn't any "automatic" procedure to find all of them. What do you think? However, I have tried...
10. ### Does (a * b) mod c = ((a mod c) * b) mod c ?

Does (a * b) mod c = ((a mod c) * b) mod c ? If so, is this a rule? I know that (a * b)%c = ((a%c) * (b%c))%c.
11. ### Prove that if x and y are both odd, then x â‰¡ y (mod 2)

1 ) Prove that if X and Y are both odd , then xâ‰¡y ( mod2 ) staff to answer is this : ANSWER: Suppose x and y are each IMP air. By definition , we can find integers a and b such that x = 2a + 2b + bey = 1. But x -y = ( 2a + 1 ) - ( 2b + 1 ) = 2a- 2b = 2 (ab ) , so that 2 | ( xy ) ...
12. ### a(n) = prime(n) mod n?

1st0 2nd1 3rd2 4th3 5th1 6th1 How do I actually do this on a calculator with the Mod button? I found this on OEIS, and it would be really useful for me if I knew more about it. Edit https://oeis.org/A004648
13. ### Question about the div and the mod

Hello everyone and good morning , I have Question about the div and the mod : If I have any of these equations what's the rules to solve it ? 1- (-2 mod 13) 2- (2 mod 13) 3- (-10 div 6) 4- (3 div 13) 5- (-3 div 13)
14. ### Navigating the Collatz Conjecture via Mod 9

Would anyone like to discuss this chart I have designed to map the deterministic path that any Collatz iterative sequence of n always follows? http://airology.blogspot.com.au/
15. ### Conjecture on period Fibonacci number mod 2^k

The period of a Fibonacci number, F_n\pmod{2^k}, is equal to 3 ( 2^{k-1}). For example, the period of F_n\pmod{2^1} is equal to 3(2^0). The period of F_n\pmod{2^2} is equal to 3(2^1). The period of F_n\pmod{2^3} is equal to 3(2^2). I can't wrap my head around why this is so.
16. ### Gauss' algorithm

in the equation for the initial equation to find the weekday of 1st January in year : (1 + 5((A-1)mod4) + 4((A-1)mod100) + 6((A-1)mod400) mod7 i understand each term represents a leap year, but i can not work out what the co - efficient are for so the 5 and 4 and 6 ?
17. ### (a^p)-(b^p)-(c^p) congruent to 0 (mod p) (with mild restrictive conditions)

Hello there, I recently found out about a very interesting relationship in number theory: Given a = b + c where a, b and c are integers, it is true that: (a^p)-(b^p)-(c^p) is congruent to 0, modulo p, for any prime p. *Note that this relationship is a general version of Fermat's...
18. ### A question regarding groups of integers mod k

It should be fairly obvious that the integers from 1 to k-1 which are relatively prime to k form a group under multiplication mod k, which I will refer to hereafter by the notation G(k). Earlier I had made the observation that if n is squarefree, then G(n) is isomorphic to a product of cyclic...
19. ### m^(Ï†(n))+n^(Ï†(m)) â‰¡ 1 mod (m n)

Hey!!!!! ;) I have to show that: \text{if } m,n \geq 1 \text{ and } (m,n)=1, \text{ then } m^{\phi(n)}+n^{\phi(m)} \equiv 1 \pmod{ m \cdot n} That's what I have tried: (m,n)=1 So,from Euler's theorem: m^{\phi(n)} \equiv 1 \pmod n \text{ and } n^{\phi(m)} \equiv 1 \pmod m...
20. ### Predict Primes with the Sixth Sense Sieve

I am an amateur mathematician with an interest in Prime Numbers and Number Theory. While investigating primes, I discovered an interesting pattern. I am interested to know if this "discovery" is already known/proven. Unfortunately, I do not know any Number Theory experts with whom to review...