n is a positive integer base from 2 to 36 inclusively.
Each of α and β is a
nonzero digit of base n from 1 to n-1 inclusively.
Determine all possible triplets (α, β, n) such that:
(α*β)base n
----------- is a positive integer.
(α.β)base n
### For example, in base ten corresponding to (α, β) = (4, 5), we observe that:
(4*5)/(4.5) = 40/9, which is NOT a positive integer.
(In reply to
computer solution by Charlie)
Code was added to eliminate unnecessary trailing zeros:
sout=sprintf('%2d %2d %2d %13.9f %13.9f %13.9f \n',a, b, n, numerator, denominator, f);
trans=false; ppos=0;
for i=1:length(sout)
switch sout(i)
case '.'
trans=true; ppos=i;
case {' ' '\n' }
if trans==true
trans=false;
for j=i-1:-1:ppos
if sout(j)>'0' && sout(j) <='9'
break
end
if sout(j)=='0'
sout(j)=' ';
else
if sout(j)=='.'
sout(j)=' ';
break
end
end
end
ppos=0;
end
end
end
fprintf('%s',sout);
The output of the bottom half was placed next to that of the top, deleting the duplicate column, to get:
decimal representation base-n rep.
-------------------------------------------------- ---------
alpha n numerator denominator result alpha
beta beta
1 3 6 3 1.5 2 1 3
2 4 6 8 2.666666667 3 2 4
2 5 10 10 2.5 4 2 5
3 6 10 18 3.6 5 3 6
1 4 12 4 1.333333333 3 1 4
1 6 12 6 1.5 4 1 6
2 8 12 16 2.666666667 6 2 8
6 9 12 54 6.75 8 6 9
3 7 14 21 3.5 6 3 7
4 8 14 32 4.571428571 7 4 8
2 6 15 12 2.4 5 2 6
4 12 15 48 4.8 10 4 C
6 10 15 60 6.666666667 9 6 A
1 9 18 9 1.5 6 1 9
2 12 18 24 2.666666667 9 2 C
4 9 18 36 4.5 8 4 9
5 10 18 50 5.555555556 9 5 A
1 5 20 5 1.25 4 1 5
2 10 20 20 2.5 8 2 A
3 12 20 36 3.6 10 3 C
3 15 20 45 3.75 12 3 F
12 16 20 192 12.8 15 C G
2 7 21 14 2.333333333 6 2 7
3 18 21 54 3.857142857 14 3 I
4 14 21 56 4.666666667 12 4 E
5 11 22 55 5.5 10 5 B
6 12 22 72 6.545454545 11 6 C
1 8 24 8 1.333333333 6 1 8
1 12 24 12 1.5 8 1 C
2 16 24 32 2.666666667 12 2 G
3 9 24 27 3.375 8 3 9
6 18 24 108 6.75 16 6 I
10 16 24 160 10.666666667 15 A G
6 13 26 78 6.5 12 6 D
7 14 26 98 7.538461538 13 7 E
1 21 28 21 1.75 12 1 L
2 8 28 16 2.285714286 7 2 8
3 14 28 42 3.5 12 3 E
4 16 28 64 4.571428571 14 4 G
6 24 28 144 6.857142857 21 6 O
15 21 28 315 15.75 20 F L
1 6 30 6 1.2 5 1 6
1 15 30 15 1.5 10 1 F
2 12 30 24 2.4 10 2 C
2 15 30 30 2.5 12 2 F
2 20 30 40 2.666666667 15 2 K
3 10 30 30 3.333333333 9 3 A
3 18 30 54 3.6 15 3 I
4 24 30 96 4.8 20 4 O
6 20 30 120 6.666666667 18 6 K
7 15 30 105 7.5 14 7 F
8 16 30 128 8.533333333 15 8 G
14 21 30 294 14.7 20 E L
20 25 30 500 20.833333333 24 K P
3 22 33 66 3.666666667 18 3 M
4 12 33 48 4.363636364 11 4 C
8 24 33 192 8.727272727 22 8 O
14 22 33 308 14.666666667 21 E M
8 17 34 136 8.5 16 8 H
9 18 34 162 9.529411765 17 9 I
1 14 35 14 1.4 10 1 E
2 28 35 56 2.8 20 2 S
2 30 35 60 2.857142857 21 2 U
6 15 35 90 6.428571429 14 6 F
12 21 35 252 12.6 20 C L
12 30 35 360 12.857142857 28 C U
1 12 36 12 1.333333333 9 1 C
1 18 36 18 1.5 12 1 I
2 9 36 18 2.25 8 2 9
2 24 36 48 2.666666667 18 2 O
4 18 36 72 4.5 16 4 I
5 20 36 100 5.555555556 18 5 K
6 27 36 162 6.75 24 6 R
21 28 36 588 21.777777778 27 L S
|
|
Posted by Charlie
on 2022-07-27 18:16:35 |
re: computer solution formatting improved
