Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Any ideas?

Prove that 3^4^5+4^5^6 is a product of two integers, each of which is larger than 10^2002.
Tried a couple of things but can't find a reasonable approach.

Original post by ValerieKR

Prove that 3^4^5+4^5^6 is a product of two integers, each of which is larger than 10^2002.
Tried a couple of things but can't find a reasonable approach.

Is this

(3^4)^5

or

3^{4^5}

?

OP

Original post by Zacken

Is this

(3^4)^5

or

3^{4^5}

?

2nd one

Original post by ValerieKR

2nd one

Write

\displaystyle 3^{4^5} + 4^{5^6}

as

m^4 + 4n^4

where you choose a suitable value for

n

, then factorise and show the smaller factor is greater than 10^(2002).

OP

Original post by Zacken

Write

\displaystyle 3^{4^5} + 4^{5^6}

as

m^4 + 4n^4

where you choose a suitable value for

n

, then factorise and show the smaller factor is greater than 10^(2002).

Thanks

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