# Tagged Questions

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### Finding which base number given operations

$$(35_a + 24_a) * 21_a = 1081_a$$ Which base is the above number? Any advice on how to solve questions like these? I tried making it in to a polynomial: $(3a+5 + 2a+4) * (2a+1) = 108a + 1$ ...
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### Are there any “obviously” true propositions in number theory?

After all efforts spent on wrong proofs of famous number theory conjectures and theorems like Goldbach's or Fermat's last theorem, could one find some simple statements (might be correct ones) whose ...
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If we use the method of contradiction(i.e.Reductio Ad Absurdum), and if one of our assumptions is wrong, does that mean that all our assumptions are wrong and is the statement or hypothesis proved?
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### Diophantine equations and Hilbert's 10th Problem, how did MRDP do it?

I'm having a bit of trouble understanding the Wiki explanation of MRDP's (Matiyasevich, Robinson, Davis, Putnam)'s Theorem, which explains that Hilbert's 10th problem is unsolvable. The MRDP ...
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### Proving that operations give equal results given equal inputs

I was reading about the 9 or 12 basic properties of 'fields' (if that's what they're called) in a book called Spivak's Calculus, 3rd Edition, and got quite befuddled by dealing with as basic stuff as ...
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My text says: Let Evens be the set of even integers greater than 2, and let Primes be the set of primes. Then we can write Goldbach’s Conjecture in logic notation as follows: $\forall n \in ... 3answers 45 views ### Logical structure of elementary number theoretic proof I'm trying to understand the detailed logic structure of a proof by use of the bezout identity.The number theoretic part i easily understand, the problem i'm having is with the logic. One example ... 1answer 184 views ### Numbers permutation Given$n$numbers and$k$positions I want the total number of permutations of these n numbers on these$k$positions if repetition is allowed and if the following two arrangements are considered ... 2answers 319 views ### There are two integers whose sum and difference are perfect squares Definition: A positive integer$m$is said to be a perfect square if there exists an integer$n$such that$m = n^2$. Write a detailed structured proof to prove that there exist two distinct ... 2answers 86 views ### Problem of Ages (Problema das Idades) English: Somebody help me with this challenge? It's very confusing: Today, both me and my younger brother are between$10$and$20$years old. Also, our ages are expressed by prime numbers and the ... 1answer 106 views ###$xy$itself square in this particular logic I would like to know the solution or procedure to find the exact analysis/solution of one of my observation. let$x = a^2$and$y = b^2$, then can we express$xy$(concatenation of$x$and$y$) as ... 1answer 48 views ### Missing one link in logic of basic unique factorization argument From page 2 of The Prime Facts : from Euclid to AKS by Scott Aaronson : Thus P/A = R/K. But R is less than P, since it’s a remainder from dividing by P. Okay So P/A can’t be in lowest ... 4answers 136 views ### If$b\mid ca$, then$b\mid a$. Is this true? My proof: We want to show$b\mid a$i.e.$a = bn$for some integer$n$. Since$b\mid ca$,$ca = bm$for some integer$m$. Substituting for$a$gives us$c(bn) = bm \Rightarrow b(cn) = bm\dots$After ... 1answer 448 views ### Gödel, Escher, Bach:$ b $is a power of$ 10 $. I’d like to verify if my formula correctly expresses that a number is a power of$ 10 $, using the$ \sf{TNT} $language provided by Hofstadter in his famous book Gödel, Escher, Bach: An Eternal ... 2answers 1k views ### Factorial (Proof by Induction) Prove by induction that$n!<n^n$for all$n>1$. So far I have (using weak induction): Base Case: Proved that claim holds for$n=2$Induction hypothesis: For some arbitrary$n>1, n!<n^n$... 3answers 848 views ### Hofstadter's TNT: b is a power of 2 - is my formula doing what it is supposed to? If you've read Hofstadter's Gödel, Escher, Bach, you must have come across the problem of expressing 'b is a power of 2' in Typographical Number Theory. An alternative way to say this is that every ... 2answers 2k views ### Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on Popular mathematics folklore provides some simple tools enabling us compactly to describe some truly enormous numbers. For example, the number$10^{100}$is commonly known as a googol, and a googol ... 2answers 453 views ### How can my proof be improved? “Let$n$be an integer. If$3n$is odd then so is$n\$.”

I am attempting to self-study proof techniques and your criticism of my following proof would be greatly appreciated. Feel free to nitpick minor/trivial things; that's how I'll learn! Edit: I have ...