[STEP][剑桥数学入学考试][03-S1-Q7][Number Theory][Multiple of 3][P1] STEP

casperyc的马甲 1月前 217

  1. Let $k$ be an integer satisfying $0\le k \le 9$.
    Show that $0\le 10k-k^2\le 25$ and that $k(k-1)(k+1)$ is divisible by $3$.
  2. For each $3$-digit number $N$, where $N\ge100$, let $S$ be the sum of the hundreds digit, the square of the tens digit and the cube of the units digit. Find the numbers $N$ such that $S=N$.

Hint: write $N=100a+10b+c$ where $a$, $b$ and $c$ are the digits of $N$.

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