[ARPAN GHOSH]

USING SINE RULE ON (ABE) AND (ADC)..WE GET BE=12

[ARPAN GHOSH]

SOLUTIONS ARE (0,0,0,2^1009),(2^1008,2^1008,2^1008,2^1008)

ANY SQUARE OF ODD IS CONGRUENT TO 1(MOD 8),SO

THE EQUATION HAS NO SOLUTION WITH AN ODD COMPONENT.

WE MUST HAVE A=2X,B=2Y,C=2Z,D=2W.PUTTING THESE VALUES WE GET

X^2+Y^2+Z^2+W^2=2^2016...CONTINUE THIS PROCESS

WE CAN PROCEED RECURSIVELY AS LONG AS RIGHT HAND SIDE IS 0(MOD8).

EVENTUALLY WE WILL ARRIVE AT L^2+M^2+N^2+P^2=4..

SOLUTIONS OF THIS EQUATION IS (1,1,1,1),(0,0,0,2)...

PUTTING THOSE VALUES WE WILL GET SOLUTIONS..

[Author]

Posts