[Python] [7] [demo experimental practice examples] [related] perfect squares

Title: An integer plus 100 after it is a perfect square, plus 168 is a perfect square, what is the number is how much?

Program analysis: can be filled in one hundred, ten digital bits are 1,2,3,4. Composition before removing all permutations arrangement conditions are not satisfied.

Assuming that the number x.

1, then: X = 100 + n- ² , X m + 100 + 168 = ²

2, calculation equation: m ² - n- ² = (n-m +) (m - n-) = 168

3, is provided: m + n = i, m - n = j, i * j = 168, i and j is an even number at least one

4, can be obtained: m = (i + j) / 2, n = (i - j) / 2, i and j are either both even or both odd.

5, 3, and 4 derived from know, I and j are both an even number greater than or equal to 2.

6, since i * j = 168, j> = 2, the . 1 <I <168/2 +. 1 .

7, all numbers next cycle i can be calculated.

Source Codes (formerly Python2.0):

This calculation method is very interesting, to be studied

My source code:

# ! / Usr / bin / Python 
# encoding = UTF-8 
# - * - Coding: UTF-8 - * - 

# Title: An integer that after 100 plus is a perfect square, plus 168 is a perfect square, what is the number is how much? 
# Problem-solving ideas: first find the approximate range of the number of Z 
#          by definition function to determine whether each of the number of perfect square, meets conditions of the subject; 

# verify whether perfect square 

Import Math
 DEF isSqr (n-): 
    A = int ((Math.sqrt (n-)))
     return a == * a n-
 # return value of the function is defined, for a perfect square, returns True, the non-perfect square returns False;     


# answer to the judgment by this cycle boundary , for the next cycle of the input parameters; 
# with the increase of a factor of t, which is the square of the difference between the square of t + 1 will be more and more, so this rule set by the cycle 
# difference between the sum of two squares full title of 168 
for the y- inrange (0,10000 ):
     IF (. 1 + Y) ** 2-Y ** 2> = 168 : 
        Z = Y 2 +. 1 **   # time range iteration, not the second parameter 
        Print ( " Y: " , Y, " Z: " , Z)
         BREAK 

# minimum value should start -100 
for I in Range (-100 , Z):
     IF I 10% in [0,1,4,5,6,9]:   # The Features fully square numbers, these are only single-digit number. 
        IF isSqr (I + 100) and isSqr (I + 268 ):
             Print (I, " ## " , (I + 100) ** 0.5,"&&&",(i+268)**0.5)

Output:

C:\Python30_demo>python 018demo.py
y: 84 z: 7057
-99 ## 1.0 &&& 13.0
21 ## 11.0 &&& 17.0
261 ## 19.0 &&& 23.0
1581 ## 41.0 &&& 43.0

A total of four numbers, -99,1,21,261,1581

-------- (I am dividing line) --------

reference:

1. RUNOOB.COM ： https://www.runoob.com/python/python-exercise-example3.html

2. https://www.cnblogs.com/zlsjjn/p/7459607.html

3. Baidu Encyclopedia: https://baike.baidu.com/item/%E5%AE%8C%E5%85%A8%E5%B9%B3%E6%96%B9%E6%95%B0/8025061? fr = aladdin

Remarks:

Initial modified: September 22, 2019 23:37:37

First Review: September 23, 2019 00:06:08 / modify the format and some duplicate content

Environment: Windows 7 / Python 3.7.2

[Python] [7] [demo experimental practice examples] [related] perfect squares

Guess you like