Return to Answer

I wrote a little program to compute $N^N \mod 1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999}$ $mod$ $1000000$ $=$ $999999$
$100001^{100001}$ $mod$ $1000000$ $=$ $100001$
$90789^{90789}$ $mod$ $100000$ $=$ $98709$
$10001^{10001}$ $mod$ $100000$ $=$ $10001$
$1001^{1001}$ $mod$ $10000$ $=$ $1001$
$1^{1}$ $mod$ $10$ $=$ $1$

$999999$ is not possible, we only have 5 $9$'s (I'll assume the $6$ won't do).

$100001$ is not possible, we only have 2 $0$'s.

$\mathbf{90789}$ is the largest working number

I wrote a little program to compute $N^N$ $mod$ $1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999}$ $mod$ $1000000$ $=$ $999999$
$100001^{100001}$ $mod$ $1000000$ $=$ $100001$
$90789^{90789}$ $mod$ $100000$ $=$ $98709$
$10001^{10001}$ $mod$ $100000$ $=$ $10001$
$1001^{1001}$ $mod$ $10000$ $=$ $1001$
$1^{1}$ $mod$ $10$ $=$ $1$

$999999$ is not possible, we only have 5 $9$'s (I'll assume the $6$ won't do).

$100001$ is not possible, we only have 2 $0$'s.

$\mathbf{90789}$ is the largest working number

I wrote a little program to compute $N^N \mod 1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999}$ $mod$ $1000000$ $=$ $999999$
$100001^{100001}$ $mod$ $1000000$ $=$ $100001$
$90789^{90789}$ $mod$ $100000$ $=$ $90789$
$10001^{10001}$ $mod$ $100000$ $=$ $10001$
$1001^{1001}$ $mod$ $10000$ $=$ $1001$
$1^{1}$ $mod$ $10$ $=$ $1$

$999999$ is not possible, we only have 5 $9$'s (I'll assume the $6$ won't do).

$100001$ is not possible, we only have 2 $0$'s.

$\mathbf{90789}$ is the largest working number

I wrote a little program to compute $N^N \mod 1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999}$ $mod$ $1000000$ $=$ $999999$
$100001^{100001}$ $mod$ $1000000$ $=$ $100001$
$90789^{90789}$ $mod$ $100000$ $=$ $98709$
$10001^{10001}$ $mod$ $100000$ $=$ $10001$
$1001^{1001}$ $mod$ $10000$ $=$ $1001$
$1^{1}$ $mod$ $10$ $=$ $1$

$999999$ is not possible, we only have 5 $9$'s (I'll assume the $6$ won't do).

$100001$ is not possible, we only have 2 $0$'s.

$\mathbf{90789}$ is the largest working number

I wrote a little program to compute $N^N \mod 1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999} \mod 1000000 = 999999$
$100001^{100001} \mod 1000000 = 100001$
$90789^{90789} \mod 100000 = 90789$
$10001^{10001} \mod 100000 = 10001$
$1001^{1001} \mod 100000 = 1001$
$1^{1} \mod 10 = 1$

999999 is not possible, we only have 5 9's (I'll assume the 6 won't do).

100001 is not possible, we only have 2 0's.

90789 is the largest working number

I wrote a little program to compute $N^N \mod 1000000$. And checked whether the last digits of the result match the digits of $N$ reversed.

I got the following solutions:

$999999^{999999}$ $mod$ $1000000$ $=$ $999999$
$100001^{100001}$ $mod$ $1000000$ $=$ $100001$
$90789^{90789}$ $mod$ $100000$ $=$ $90789$
$10001^{10001}$ $mod$ $100000$ $=$ $10001$
$1001^{1001}$ $mod$ $10000$ $=$ $1001$
$1^{1}$ $mod$ $10$ $=$ $1$

$999999$ is not possible, we only have 5 $9$'s (I'll assume the $6$ won't do).

$100001$ is not possible, we only have 2 $0$'s.

$\mathbf{90789}$ is the largest working number