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Why is an octal number the result of dividing a decimal number by 8 and getting the remainders?

Octal is to 8 what decimal is to 10, hexadecimal is 16, and binary is to 2. When you write the number ten in decimal, you write 10, which is the same as 1*10^1 + 0 * 10^0. In binary, it's 1010: 1 * 2^...
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How to integrate bessel function with variable bounds?

TL;DR You are facing two problems: Wrong call of quad which requires a function not a number; Missing vectorization to recompute your integral for each x. MCVE Here a MCVE slightly adapting your ...
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Goldbach's Conjecture - Find the number of ways an even number can be written as the sum of two primes

For 1 billion I get 2274205 for 100,000 I get 291400. This result is the same as the sieve above. Except this is brute force. This code is way slower than the sieve of 6k numbers. Tried this to ...
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Fast but accurate trigonometric modulo range reduction for moderate magnitude inputs

The method of fast reduction of trigonometric functions using the sine function as an example is described in the article "Fast argument reduction of the sine function based on assembly ...
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Subtracting a large unsigned binary number from a smaller one

0101 0111 1101 (1405)_10 -1110 1011 0110 - (3766)_10 0110 1100 0111 (-2361)_10 If we(2's) complements the answer then we find the decimal equivalent answer. such, 0110 1100 0111 &...

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