Proof: the remainder of a complete square divided by 9 can only be 0 or 1 or 4 or 7

Let X be a complete square number. It is easy to know that there exists positive integer P such that x = P & # 178; and all positive integers can be divided into nine categories: A & # 8319; = {P | P = 9p + N, P ∈ Z +, n = 0,1,2,3,8} x = P & # 178; = (9p + n) &# 178; = 9 (9p & # 178; + 2pn) + n & # 178;. N & # 178;. I 0 01 1 12 4 43 9 04

Prove: even number square divided by 8, the remainder is 0 or 4, odd number square divided by 8, the remainder is 1

Even numbers can be written as: 2n + 2 (n is an integer) the square of even numbers is divided by 8; (2n + 2) &# 178; △ 8 = 4 (n + 1) &# 178; △ 8 because 4 (n + 1) &# 178; must be a multiple of 4, so: the remainder of the above formula is 0 or 4 odd numbers can be written as: 2n + 1 (n is an integer) the square of odd numbers is divided by 8: (2n + 1) &# 178; △ 8 = (4N & # 178

Write all numbers with the same quotient and remainder (not 0) as 7______ ．

When the remainder sum quotient is 6: 6 × 7 + 6 = 48, when the remainder sum quotient is 5: 5 × 7 + 5 = 40, when the remainder sum quotient is 4: 4 × 7 + 4 = 32, when the remainder sum quotient is 3: 3 × 7 + 3 = 24, when the remainder sum quotient is 2: 2 × 7 + 2 = 16, when the remainder sum quotient is 1: 1 × 7 + 1 = 8

What is the remainder of a nonzero number divided by 4

0.1.2.3.

The remainder of 333 ········ 33 (100 3) divided by 13 is () 81547 times 118 divided by 7
The remainder of 9642 times 2879 times 4787 divided by 13 is ()
The remainder of 2461 * 135 + 6047 * 323-2345 divided by 11 is ()
253 to the 16th power * 127 to the 19th power + 37 to the 52nd power * 136 to the 62nd power divided by 9 is ()

The remainder of the first question divided by thirteen is 8, and the second question is 4

In a division with remainder, the sum of divisor, divisor and quotient is 73. The sum of divisor and quotient remainder is 17. Given that quotient is 8, how to find the divisor?

Let the divisor be y, the remainder be Z, and the divisor be X
y+x+8=73 __ (1)
x+8+z=17 __ (2)
y=8*x+z __ (3)
The solution of the equations is x = 7, z = 2, y = 58
The idea of doing the program is different. This is how to do it
#include "stdio.h"
void main()
{
int y,x,z;
for(y=0;y

In a division formula, the sum of divisor, divisor, quotient and remainder is 1063. Given that quotient is 36 and remainder is 17, find the divisor

Data error, and changed to 1069 is just right
Known:
Divisor + divisor + quotient + remainder = 1069
The known quotient is 36 and the remainder is 17
obtain:
Divisor + divisor = 1069-17-36 = 1016
Because the divisor is 17 times more than 36 times the divisor
So:
Divisor = (1016-17) / (36 + 1) = 27
Divisor = 27 × 36 + 17 = 989

In a division where the divisor is one digit, if the quotient is 25 and the remainder is 8, what is the divisor?

233
If the remainder is 8, the divisor must be greater than 8,
Divisor is a single digit number
It can only be nine
Divisor = 9 * 25 + 8 = 233

The quotient of a division formula is 16, the remainder is 25, what is the minimum divisor, and what is the divisor?

According to the meaning of the question, the remainder is 25, so the divisor must be greater than or equal to 26, and the one that meets the condition can only be the minimum when 26, so the divisor at this time = 26 * 16 + 25 = 441
A: the minimum divisor is 26, and the divisor is 441

In a division formula with remainder, the sum of divisor, divisor, quotient and remainder is 594, the known quotient is 16, the remainder is 17, and the number of divisors in the problem is many
It is

Divisor = 16 * divisor + 17
Divisor + divisor = 594-16-17-17 = 544
Divisor = 544 / (1 + 16) = 32
The divisor is 32

Proof: the remainder of a complete square divided by 9 can only be 0 or 1 or 4 or 7