Find 2 positive integers greater than 1 whose product is #6^6 + 8^4 + 27^4#?

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Answer 1 · 2017-07-27T01:21:38

See a solution process below:

#6^6 = 46,656#

#8^4 = 4,096#

#27^4 = 531,441#

Therefore:

#6^6 + 8^4 + 27^4 = 46,656 + 4096 + 531,441 = 582,193#

#582,193 = 577 xx 1009#

Answer 2 · 2017-07-27T09:21:50

#6^6+8^4+27^4=577*1009#

Calling #a = 3^6# and #b = 2^6# we have

#6^6+8^4+27^4=a*b+b^2+a^2 = (a+b)^2-a*b# or using the identity

#u^2-v^2=(u-v)(u+v)#

#(2^6+3^6)^2-(2^3*3^3)^2 = (2^6+3^6-2^3*3^3)(2^6+3^6+2^3*3^3)# or

#6^6+8^4+27^4=577*1009#