코딩 연습

We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by \(7\): 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 However, if we check the first one hundred rows, we will find that only \(2361\) of the \(5050\) entries are not divisible by \(7\). Find the number of entries which are not divisible by \(7\) in the first one billion \(\l..

In a\(3 \times 2\) cross-hatched grid, a total of \(37\) different rectangles could be situated withing that grid as indicated in the sketch. There are \(5\) grids smaller than \(3 \times 2\), vertical and horizontal dimensions being important, i.e. \(1 \times 1\), \(2 \times 1\), \(3 \times 1\), \(1 \times 2\) and \(2 \times 2\). If each of them is cross-hatched, the following number of differe..

The smallest positive integer \(n\) for which the numbers \(n^2 +1\), \(n^2 +3\), \(n^2+7\), \(n^2+9\), \(n^2+13\), and \(n^2+27\) are consecutive primes is \(10\). The sum of all such integers \(n\) below one-million is \(1242490\). What is the sum of all such integers \(n\) below \(150\) million? \(n^2 +1\), \(n^2 +3\), \(n^2+7\), \(n^2+9\), \(n^2+13\), \(n^2+27\) 이 연속적인 소수가 되는 최소의 자연수 \(n\) 은..