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# ISSUES

Problems in Elementary Number Theory 1 [ 2008 ] No. 1

K12, H15, O53, I11, J11, A03, D02, O35, B06, O49

Problems in Elementary Number Theory 2 [ 2009 ] No. 1

K11, I10, A14 & A71, N17, D05 & D06 & (M16), C2, (Q7), A13, A23 & A24, E16, A37 & A9 & O51

Problems in Elementary Number Theory 2 [ 2009 ] No. 2

will be weblished around December, 2009.

### 22 Responses

1. Great.Keep it up!

2. […] I […]

3. […] PEN: Editors-in-Chief for 2010 By compactorange As you know, Problems in Elementary Number Theory 2 [ 2009 ] No. 1 is NOW […]

4. […] I […]

5. Hello ! My name is phalkun lim . I live in Cambodia !
I have a problem in Mathematics ! Please solving to me !

Find numbers x= H U N S E N and y = S T R O N G
if H U N S E N x 3 = S T R O N G

Thanks!

6. 126356 E=5 G=8 H=1 N=6 O=0 R=9 S=3 T=7 U=2
126356
+126356
——-
379068

318928 E=2 G=4 H=3 N=8 O=7 R=6 S=9 T=5 U=1
318928
+318928
——-
956784

7. Thanks! Andrew.

8. […] Project PEN […]

9. Compute the sum

S=1X9+2X99+3X999+4X9999+…….+n (999…..999)

10. S = 1(10 – 1) + 2(100 – 1) + … + n(100…n zeroes – 1)
S = 1(10^1) + 2(10^2) + … + n(10^n) – (1 + 2 + … + n)
Now let S = P + Q
where P = 1(10^1) + 2(10^2) + … + n(10^n) and Q = (1 + 2 + … + n) = n(n + 1)/2
Now 10P = 1(10^2) + 2(10^3) + … + n(10^n+1)

=> 9P = -(10^1 + 10^2 + … + 10^n) + n(10^n+1)
=> P = n(10^n+1)/9 – 10(10^n – 1)/81

12. Let A , B , C are arithmetic sequence and N= ACB is perfect squares.
Find A , B , C
(0<A<9,0<B<9,0<C<9)

• A = 5, B = 6, C = 7 and ACB = 576 = 24^2

13. thanks

14. Hello ! today I have some problems !

I- find all functions f:IN to IR that :
f(0)=f(1)=f(2)=3 and f(n+3)=3f(n+2)-3f(n+1)+f(n)+2n+3
II-Let f(n) for n=1 , 2 , 3 , ….
f(1)=257/16 , f(2)=65/8 and f(n+2)=(5/2) f(n+1)-f(n) .
find n if f(n) minimum ?
III-Find of Sum :
S=1!1.2+2!2.3+3!3.4+4!.4.5+….+n!n(n+2)
IV-find all n on IN if n(n+1)(n+2) devised by 7 .
V- find a , b , c , d , e if abcde X 4 = edcba

• V – 21978 * 4 = 87912.
IV – n = 0, -1, -2 mod7.

15. find all a and b in IN and a different b such that aaaaab =0 (mod 7 )

• b – a = 0 mod7
As a and b are different integers, we can have (a, b) = (9, 2), or (8, 1).

16. Compute the sum :
S=a+aa+aaa+aaaa+….+aaa….aaaa

17. Find a such that : 21a78|87a12 ?