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set with maximum sum consisting of mutually co-prime numbers

Definitions. Let $n$ be a natural number and $S$ be a subset of distinct natural numbers all less than $n$, and mutually co-prime. Then find the maximum sum the set $S$ can have. Example. Let $n=10$, ...
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What is the fastest way to check if an integer is divisible by another?

What would the Big O be? Can something like this be done in O(log(n)) where n is the number of bits?
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Use of sorting in counterexamples for equations

I came across a question which asked how sorting would help in searching for counterexamples to the conjecture that $$u^6 + v^6 + w^6 + x^6 + y^6 = z^6$$ has no non trivial solutions in integers. The ...
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Difference between the definitions regarding distribution of prime numbers [migrated]

Following are the two theorems that Hardy and Wright state in their book Theorem A: The number of primes not exceeding $x$ is given by $\pi(x) \sim \frac{x}{\log{x}}$. Theorem B: The order ...
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Numerical stability of linear interpolation

Is one of these two functions more numerically stable than the other? ...
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Josephus Problem - A faster Solution

I came through Josephus problem a little while ago. Problem is stated as follows : "People are standing in a circle waiting to be executed. Counting begins at a specified point in the circle and ...
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How to compute the sum of this series involving golden ratio, efficiently?

Definitions Let $\tau$ be a function on natural numbers defined as $\tau(n)=\lceil n*\phi^2\rceil$ where $n$ is some natural number and $\phi=\frac{1+\sqrt{5}}{2}$ is the golden ratio. This series ...
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Why is the set of perfect squares in P?

I am reading an article by Cook [1]. In it he writes: The set of perfect squares is in P, since Newton's method can be used to efficiently approximate square roots. I can see how to use Newton's ...
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Computing losing positions in modified Wythoff's game efficiently

Wythoff's game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of stones. When his turn a player can remove one or more stones from anyone pile ...
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Reccurrence for the game of pile of stones

I am trying to solve this question from Project Euler for past few days: Divisor game. The problem is as follows: Two players are playing a game. There are $k$ piles of stones. When it is his turn ...
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Convert integer of mixed radix to standard positional numeral system and vice versa

I have multiple numbers (e.g. [1, 4, 2]) where each number can be one of a specified range of numbers (e.g. [0-1, 0-5, 0-3]). I ...
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Finding all “smooth” numbers up to 10^6 — problem with nested loops [duplicate]

A [smooth number] is one whose factors are all "small". For a computational problem, I would like all smooth numbers up to $10^8$. I think it's unfeasible to factor a billion numbers. Instead, I ...
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How can I generate first n elements of the sequence 3^i * 5^j * 7^k?

How can I efficiently generate the first N elements of the sequence $3^i 5^j 7^k$, where $i,j,k \in \mathbb{N}$? I've googled around a bit and found the sequence in OEIS, but I don't really see a ...
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Introduction to number theory [closed]

What is the best book for a beginner in Introduction to number theory? I am new to this field and getting deeper into cryptography, so I think reading some intro books about number theory can be of ...
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What is complexity of checking whether a natural number is a perfect square? [closed]

As the title says, what is complexity of checking whether a natural number is a perfect square?
Given a number N, and some set $A=\{a, 1\le a\le N\}$, and let $B=\{\text{every integer} \in [1,N]\}$, and $C=B\setminus A$ (Set C has all values from B not in A) What is the best way of finding the ...