Amicable Quadruple
المؤلف:
Guy, R. K.
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
p. 59
22-11-2020
804
Amicable Quadruple
An amicable quadruple as a quadruple 
such that
 |
(1)
|
where 
is the divisor function.
If 
and 
are amicable pairs and
 |
(2)
|
then 
is an amicable quadruple. This follows from the identity
 |
(3)
|
The smallest known amicable quadruple is (842448600, 936343800, 999426600, 1110817800).
Large amicable quadruples can be generated using the formula
![[a; b; c; d]=C_n[173·1933058921·149·103540742849; 173·1933058921·15531111427499; 336352252427·149·103540742849; 336352252427·15531111427499],](https://mathworld.wolfram.com/images/equations/AmicableQuadruple/NumberedEquation4.gif) |
(4)
|
where
 |
(5)
|
and 
is a Mersenne prime with 
a prime 
(Y. Kohmoto; Guy 1994, p. 59).
REFERENCES:
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 59, 1994.
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