How to resolve the algorithm Euler's sum of powers conjecture step by step in the 360 Assembly programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Euler's sum of powers conjecture step by step in the 360 Assembly programming language
Table of Contents
Problem Statement
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. This conjecture is called Euler's sum of powers conjecture and can be stated as such: In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a CDC 6600 computer restricting numbers to those less than 250. The task consists in writing a program to search for an integer solution of
x
0
5
x
1
5
x
2
5
x
3
5
=
y
5
{\displaystyle x_{0}^{5}+x_{1}^{5}+x_{2}^{5}+x_{3}^{5}=y^{5}}
where all
x
i
{\displaystyle x_{i}}
and
y
{\displaystyle y}
are distinct integers between 0 and 250 (exclusive). Show an answer here. Related tasks are:
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Euler's sum of powers conjecture step by step in the 360 Assembly programming language
Source code in the 360 programming language
EULERCO CSECT
USING EULERCO,R13
B 80(R15)
DC 17F'0'
DC CL8'EULERCO'
STM R14,R12,12(R13)
ST R13,4(R15)
ST R15,8(R13)
LR R13,R15
ZAP X1,=P'1'
LOOPX1 ZAP PT,MAXN do x1=1 to maxn-4
SP PT,=P'4'
CP X1,PT
BH ELOOPX1
ZAP PT,X1
AP PT,=P'1'
ZAP X2,PT
LOOPX2 ZAP PT,MAXN do x2=x1+1 to maxn-3
SP PT,=P'3'
CP X2,PT
BH ELOOPX2
ZAP PT,X2
AP PT,=P'1'
ZAP X3,PT
LOOPX3 ZAP PT,MAXN do x3=x2+1 to maxn-2
SP PT,=P'2'
CP X3,PT
BH ELOOPX3
ZAP PT,X3
AP PT,=P'1'
ZAP X4,PT
LOOPX4 ZAP PT,MAXN do x4=x3+1 to maxn-1
SP PT,=P'1'
CP X4,PT
BH ELOOPX4
ZAP PT,X4
AP PT,=P'1'
ZAP X5,PT x5=x4+1
ZAP SUMX,=P'0' sumx=0
ZAP PT,X1 x1
BAL R14,POWER5
AP SUMX,PT
ZAP PT,X2 x2
BAL R14,POWER5
AP SUMX,PT
ZAP PT,X3 x3
BAL R14,POWER5
AP SUMX,PT
ZAP PT,X4 x4
BAL R14,POWER5
AP SUMX,PT sumx=x1**5+x2**5+x3**5+x4**5
ZAP PT,X5 x5
BAL R14,POWER5
ZAP VALX,PT valx=x5**5
LOOPX5 CP X5,MAXN while x5<=maxn & valx<=sumx
BH ELOOPX5
CP VALX,SUMX
BH ELOOPX5
CP VALX,SUMX if valx=sumx
BNE NOTEQUAL
MVI BUF,C' '
MVC BUF+1(79),BUF clear buffer
MVC WC,MASK
ED WC,X1 x1
MVC BUF+0(8),WC+8
MVC WC,MASK
ED WC,X2 x2
MVC BUF+8(8),WC+8
MVC WC,MASK
ED WC,X3 x3
MVC BUF+16(8),WC+8
MVC WC,MASK
ED WC,X4 x4
MVC BUF+24(8),WC+8
MVC WC,MASK
ED WC,X5 x5
MVC BUF+32(8),WC+8
XPRNT BUF,80 output x1,x2,x3,x4,x5
B ELOOPX1
NOTEQUAL ZAP PT,X5
AP PT,=P'1'
ZAP X5,PT x5=x5+1
ZAP PT,X5
BAL R14,POWER5
ZAP VALX,PT valx=x5**5
B LOOPX5
ELOOPX5 AP X4,=P'1'
B LOOPX4
ELOOPX4 AP X3,=P'1'
B LOOPX3
ELOOPX3 AP X2,=P'1'
B LOOPX2
ELOOPX2 AP X1,=P'1'
B LOOPX1
ELOOPX1 L R13,4(0,R13)
LM R14,R12,12(R13)
XR R15,R15
BR R14
POWER5 ZAP PQ,PT ^1
MP PQ,PT ^2
MP PQ,PT ^3
MP PQ,PT ^4
MP PQ,PT ^5
ZAP PT,PQ
BR R14
MAXN DC PL8'249'
X1 DS PL8
X2 DS PL8
X3 DS PL8
X4 DS PL8
X5 DS PL8
SUMX DS PL8
VALX DS PL8
PT DS PL8
PQ DS PL8
WC DS CL17
MASK DC X'40',13X'20',X'212060' CL17
BUF DS CL80
YREGS
END
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