Equal Sums of Like Powers

Non-negative Integer Solutions of

• No solution seems to have appeared in the literature.
• Soltions of this type can be easily found by computer. Here are some smallest solutions ( max { a_i, b_i }<50 ) obtained by Chen Shuwen using a 386SX PC in 1995.
• [ 3, 25, 38 ] = [ 7, 20, 39 ]
• [ 15, 36, 39 ] = [ 22, 25, 43 ]
• [ 4, 36, 43 ] = [ 9, 28, 46 ]
• [ 4, 41, 42 ] = [ 11, 28, 48 ]
• A solution chain of this type, by Chen, using a Pentium PC
• [ 24, 201, 216 ] = [ 66, 132, 243 ] = [ 73, 124, 244 ] 
• Chen Shuwen obtained a parametric solution of this type in July 1997. Numerical examples are:
• [ 31, 199, 244 ] = [ 73, 139, 262 ]
• [ 63, 163, 290 ] = [ 75, 149, 292 ]
• [ 32, 294, 463 ] = [ 116, 196, 477 ]