which digit doesn't occur in this number?

I came across this question on a site and I didn't find any solution to this.....(except to use calculator)

The question was

Which digit doesn't occur in the number 2^29 ?

Plz help.....

#NumberTheory

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Comments

If 2^29=n (mod 9),then 9-n is the answer. Noticing that 2^3=-1(mod 9),2^29=(2^3)^9x2^2=(-1)^9x2^2=-4=5 (mod 9). Therefore the answer is 9-5=4. This can be easily derived using mod. Hope you got it :)

Krishna Ar - 7 years ago

Ohh...use of mod didn't strike me :P

I was trying to solve it using logs etc. . :P

Btw...thanks you sir

Poonayu Sharma - 7 years ago

You're welcome :D....but you're 3 yrs elder, so you must refrain from calling me sir, how could you? And this solution is also inspired by an experiment I did with the cyclicity of digital roots of powers of 2. You could check out my easy-peasy problem on that though :)

Krishna Ar - 7 years ago

@Krishna Ar – U deserved "sir" :D.....and I solved the problem u talking about....but not with the (mod 9) method But with cyclic sum of digits of powers of 2

Poonayu Sharma - 7 years ago

@Poonayu Sharma – Oh. Well at first ( when I encountered this problem in class 7) I solved this using cyclicity too :)

Krishna Ar - 7 years ago

@Krishna Ar – Ohh...well dont u think it becomes a herculean task for a 7 grade guy to do such sums :P

Poonayu Sharma - 7 years ago

@Poonayu Sharma – @Poonayu Sharma - Woah! I'm mind -blown!!!! How did you level up in Algebra and Number Theory so soon? What resources did you use to gain here?