为什么4divides n^2 imply 4 divides n是错的
时间: 2024-06-04 09:09:39 浏览: 16
这个结论是错误的。如果 $4$ 整除 $n^2$,那么 $n^2$ 一定是偶数,因为 $4$ 是偶数。同时,偶数的平方也一定是偶数。因此,$n^2$ 可以表示为 $2k$,其中 $k$ 为整数。进一步可以得出 $n^2$ 是 $4$ 的倍数,即 $n^2 = 4m$,其中 $m$ 为整数。因此 $n^2$ 是偶数且是 $4$ 的倍数,那么 $n$ 也一定是偶数且是 $4$ 的倍数。因此,结论 $4$ 整除 $n^2$ 蕴含 $4$ 整除 $n$ 是正确的。
相关问题
. Prove the following: Let a, b, c, n E Z, where n 2 2. If ac = bc (mod n) and gcd(c, n) = 1,then a = b (mod n)
To prove that a = b (mod n), we need to show that n divides (a - b).
Since ac = bc (mod n), we have n divides (ac - bc) = c(a - b).
Since gcd(c, n) = 1, we know that n and c are coprime, which means that n does not divide c.
Therefore, n must divide (a - b), which means that a = b (mod n).
Hence, the statement is proved.
use C program Write a function digit(n, k) that returns the k th digit (from the right) in n (a positive integer). For example digit(829, 1) returns 9, digit(829, 2) returns 2 and digit(829, 3) returns 8. if k is greater than the number of digits in n , have the function return 0.
Sure, here's a C program that defines a function `digit(n, k)` that returns the `k`th digit (from the right) in `n` (a positive integer):
```c
#include <stdio.h>
int digit(int n, int k) {
int count = 0;
while (n > 0) {
count++;
if (count == k) {
return n % 10;
}
n /= 10;
}
return 0;
}
int main() {
int n = 829;
int k = 1;
printf("The %dth digit (from the right) in %d is %d\n", k, n, digit(n, k));
k = 2;
printf("The %dth digit (from the right) in %d is %d\n", k, n, digit(n, k));
k = 3;
printf("The %dth digit (from the right) in %d is %d\n", k, n, digit(n, k));
k = 4;
printf("The %dth digit (from the right) in %d is %d\n", k, n, digit(n, k));
return 0;
}
```
This program defines a function `digit(n, k)` that takes two arguments: `n` (the positive integer) and `k` (the index of the digit to return, from the right). The function works by counting the number of digits in `n` as it repeatedly divides `n` by 10. If `count` equals `k`, the function returns the last digit of `n`. If `count` exceeds the number of digits in `n`, the function returns 0.
I hope that helps! Let me know if you have any further questions.