Integer Definition and 620 Threads

I have 2 questions. 1)what is the remainder with 100! is divided by 103? explain your answer 2)a = 238000 = 2^4 x 5^3 x 7 x 17 and b=299880 = 2^3 x 3^2 x 5 7^2 17. Is there an integer so that a divides b^n? if so what is the smallest possibility for n? the first one i have no...

Hello all, I've been asked for a graduate level course to do a proof using induction that shows that nCr always turns out to be an integer. I thought that I might use Pascal's triangle somehow and the fact that nCr is equal to n! / r!(n-r)! (I saw a brief explanation of this while doing a web...

I have my question and my problem in the attachment that followed.

Hai COuld you please help the formula as I am not able to identify the question below: Question: For a Traingle with a perimeter of 30cm, what is the integer value of the longest possible side ? REgards aprao

Can anybody explain what appear to be discrepancies in the way the following expressions are interpreted by Hugs (Haskell98 mode) ? Main> div -6 4 ERROR - Cannot infer instance *** Instance : Num (b -> a -> a -> a) *** Expression : div - fromInt 6 4 Main> div (-6) 4 -2 Main> -6...

I just completed Trigonometry and College Algebra, and I'm heading into Calculus, so i thought i would get a head start on the material. So right now I'm working out of an old calculus book i got at the library. Then i came across this problem: A dial-direct long distance call between two...

for n- fixed integer prove that phi(x)=n has a finite number of solutions I looked at 2 cases when x is even and when x is odd 1) if x is even then phi(2x)>phi(x) and I showed why it has a finite number of solutions 2) I'm not sure how to show for the case when x is odd.. any ideas? thanks :)

The terms of this series are reciprocals of positive integers whose only prime factors are 2s and 3s: 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+... Show that this series converges and find its sum. this is my first time writing here. i hope someone can help me with this question.

How many pairs of positive integer a, b are such that a^2 + b^2 = 121?

I'm not a very logical person, and I would hardly consider math a strength so, I'm stuck with these proofs: 1. Prove that every positive integer, ending in 5 creates a number that when squared, ends in 25 2. Prove that if n is an even positive integer, then n^3 - 4n is always divisible by...

I am having trouble with this one... Prove that any positive integer whose ALL digits are 1s (except 1) is not a perfect square.

I have an integer A and a possitive odd integer B, can you tell me how to find a nonnegative integer C such that C<2^A and 1+BC=0(mod 2^A) ? ?

"x is an integer" "x is an integer" is a sentential function, right?

The Q is: show that the number of partitions of n within Z+ where no summand is divisible by 4 equals the number of partitions of n where no even summand is repeated Here is what I got so far Let the partition where no summand is divisible by 4 be P1(x) Let the partition where no even...

Is it possible to solve a radical equation where the root is a negative integer?

What does x=pmodn mean where x,p,are integers and n is a natural number?

Seem to remember reading about RF experimenting with non-integer differentiation. I found it quite interesting to play with. I started with 'half' differentiation. e.g. f(x) = x^2 , D[1]f = 2x , D[2]f = 2 but what about non-integer diff? e.g. D[0.5]f = px^1.5 what is p? Clearly...

What is the greatest integer divides p^4 -1 for every prime number p greater than 5? It is 240. Why? Thanks!

I really need someone to answer this by tomorrow 12/01 10:50 am pacific time... 1) Derive the following, for any integer k. infinity SUM OF: 1/(n^(2k)) = ((2(pi))^(2k)(-1)^(k+1)B2k ) /(2(2k)!) n=1 where Bn is defined by the following, for |x| < 2(pi). ````````````infinity (x)/(e^(x)-1)...

if a^k =1 and a \in \mathbb{C} k \in Z^+ and for some k A = \{a|a^k = 1\} does |A| = k ? edited: becasue the real numbers are a subset of the complex numbers