Find the last digit of 7^2007
my answer is 8,is it correct??
Re: Find the last digit of 7^2007
Your answer is incorrect, because $7^{2007}$ is clearly an odd number and so its last digit must be odd. How did you find it?
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: Find the last digit of 7^2007
can u plz show me the solution??
Re: Find the last digit of 7^2007
$2007\equiv3\pmod4$ and the last digit of $7^3$ is $3$, so the answer is $3$.Mathlover wrote:my answer is 8,is it correct??
Think why it works.
One one thing is neutral in the universe, that is $0$.
Re: Find the last digit of 7^2007
@Masum: Why don't you stop ruining the problems for them and let them solve the problems?
Can you find the remainder when $7^{2007}$ is divided by $10$?Mathlover wrote:can u plz show me the solution??
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: Find the last digit of 7^2007
For their thinking why it should work. This would lead them to the solution as well as a new idea.nayel wrote:@Masum: Why don't you stop ruining the problems for them and let them solve the problems?
One one thing is neutral in the universe, that is $0$.
Re: Find the last digit of 7^2007
How do you even know he/she knows what mod is?
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: Find the last digit of 7^2007
Okay. I personally think that the best idea is to give them some hints (for the easy problems)/hide the solution. However, when some relatively problem is posted you may choose to post solution normally.
BTW hiding is really easy. Just try
BTW hiding is really easy. Just try
Code: Select all
[h] your text inside [/h]
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
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Re: Find the last digit of 7^2007
$7^2 \equiv -1(mod 10) $
or,$7^{2006} \equiv -1(mod 10) $
it follows $7^{2007} \equiv -7(mod 10)$.so,$7^{2007} \equiv 3(mod 10)$
so the last digit is $3$
or,$7^{2006} \equiv -1(mod 10) $
it follows $7^{2007} \equiv -7(mod 10)$.so,$7^{2007} \equiv 3(mod 10)$
so the last digit is $3$
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Re: Find the last digit of 7^2007
the problem can be solved without using modular arithmetic. the last digit of 7^1 is 7, for 2 its 9, for 3 its 3, for 4 its 1 and for 5 its again 7.as we can write 2007 like that ….4*501+3……the last digit of 7^2007 will be the last digit of 7^3, no need of mod.