Integer Solutions
of
a1h
+ a2h + a3h
+ a4h+ a5h
= b1h + b2h
+ b3h + b4h
+ b5h
( h = 1, 2, 3, 5,
7 )
- The first solutions of this type was obtained
by G.Palama in 1953.[19] However,
it is difficult to find another example by his method.
- [ -59, -5, -1, 33, 57 ] = [ -55, -23, 13, 39,
51 ]
- Chen Shuwen checked all the known non-negative
integer solutions of the system ( k = 1, 3, 5, 7 )
with the help of a personal computer, and obtained several new solutions
of ( h = 1, 2, 3, 5, 7 ) in integers.
- [ -55, -11, 3, 37, 51 ] = [ -53, -19, 9, 43,
45 ]
- [ -71, -33, 11, 15, 73 ] = [ -57, -53, 1, 39,
65 ]
- [ -99, -13, 0, 34, 98 ] = [ -82, -58, 16, 69,
75 ]
- [ -169, -31, 103, 17, 163 ] = [ -157, 47, -71,
121, 143 ]
- [ -169, -31, 103, -47, 157 ] = [ -163, -17, -71,
121, 143 ]
Last revised March,31, 2001.
Copyright 1997-2001, Chen Shuwen