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acoustics algorithm applications approximation arithmetic array asymptotic binary calculator Chap Check Chinese Remainder Theorem coefficients composite concert hall concert hall acoustics constructed Continued Fractions convolution correlation course cyclotomic decimal decrypting defined diffraction Diophantine equations distribution divide divisible divisor function elements equal Euler example exponent fact Farey fractions Fermat primes Fibonacci numbers finite number formula Fourier transform frequency Galois sequence Gauss geometric given Golden ratio greatest common divisor inverse irreducible polynomial knapsack large numbers linear logarithm mathematical Mersenne primes Mobius function modp modulo multiplication notation number field number theory obtained pairs partitions peak factor pearls perfect numbers period length positive integer power spectrum primality testing prime factors prime number primitive root probability problem properties public-key encryption quadratic residue random recursion result Sect shown in Fig Sino-representation solution squarefree strong pseudoprimes waveforms zero