Art of Problem Solving Volume 1
... Even at this early stage in understanding divisibility, we can find some tricks to tell if one number divides another. We start with the obvious example: a number is divisible by 10 if and only if its last digit is 0. This seems trivial, but then so will the rest of the rules in this section when yo ...
... Even at this early stage in understanding divisibility, we can find some tricks to tell if one number divides another. We start with the obvious example: a number is divisible by 10 if and only if its last digit is 0. This seems trivial, but then so will the rest of the rules in this section when yo ...
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... The Goldbach partitions of 420 cover all primes in the range [n/2, n − 2] excepting 277, 251 and 233. In the case of n = 630, all primes in the corresponding range are covered excepting these eight cases: 509, 487, 461, 443, 421, 409, 383, and 331. 3. Goldback Circles and Ellipses Let 2n = p + q, as ...
... The Goldbach partitions of 420 cover all primes in the range [n/2, n − 2] excepting 277, 251 and 233. In the case of n = 630, all primes in the corresponding range are covered excepting these eight cases: 509, 487, 461, 443, 421, 409, 383, and 331. 3. Goldback Circles and Ellipses Let 2n = p + q, as ...
