Click to Chat

0120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 550 off
USE CODE: SSPD25

Show that 1993-1399 is a positive integer divisible by 162.

7 years ago

Share

Both 19^93 and 13^99 are odd, so odd – odd is even and is divisible by 2, so it’s enough we need to show that 19^93 and 13^99 is divisible by (162 / 2) which is 81.

Now, 19^93 (modulo 81) = (18 + 1)^93 (modulo 81) = 93(18) + 1 = 55 (modulo 81)

Similarly, 13^99 (modulo 81) = (12 + 1)^99 (modulo 81) = 99(12) + 1 = 1189 (modulo 81) = 55 (modulo 81)

Hence, 19^93 – 13^99 = 0 (modulo 81)

Therefore, 19^93 and 13^99 is divisible by 162
7 years ago

# Other Related Questions on Algebra

modulus operator is a bit tough for me and i cant understand a thing in some questions for eg lim x->0- mod(x)/x=-1; how does this work mod must always be positive right?

Posting again as the there is bug in website which does not properly dispay inequalities. Its not difficult if you visualise it graphically. Search google for desmos graphing calculator and ...

 Ajay 2 months ago

Its not difficult if you visualise it graphically. Search google for desmos graphing calculator and plot the graph for this function y= mod(x)/x. You will see why left hand limit for thins...

 Ajay 2 months ago
In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??

The value of gamma is still not correct, either printing mistake or you gave me wrong value. The correct value of gamma is below

 Ajay 2 months ago

Thankyou so much............................. …......................................................................!

 Anshuman Mohanty 2 months ago

Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7

 Anshuman Mohanty 2 months ago
I am not getting the derivation of the formula nPr=n!÷(n-r)!. n=no. of objects and r=no. of times taken (the object)

Consider that you have three drawers and 10 balls of different colors. Now in how many ways can you fill all three drawers with balls from set of 10 balls so that each drawer conatins one...

 Ajay 3 months ago

 riya 3 months ago
What is ((Lim n tends to infinity)(summation from r=1 to n)((r)/(n^2 +n + r)))

Please check the question it should be (r)/(n^2 +n * r))) If this is the question then we can solve by applying definite integration as a limit of sum Thanks

 Nishant Vora one month ago

 jagdish singh singh one month ago
find the derivative of abs(x-3) when x = -1 with correct steps

Hii you have to draw the curve and once you draw it you will see that the slope of the tangent is -1

 Sourabh Singh 2 months ago

By definition the modulus function is defined as = -x+3 Hence derivative = -1 for all values of x less than 3 which includes -1

 Ajay 2 months ago
find the distance A(2,3) measured parallel to the line x-y=5 from the line 2x+y+6=0

given equation x-y=5 and 2x+y+6=0 x=5+y..... eq1 2(5+y)+y+6 10+2y+y+6=0 y=-16/3 and x=-1/3 Now, distance between A and (x,y)is root under (x2-x1) +(y2-y1)2 hence distance =8.05

 Muna Kunwar one month ago
View all Questions »

• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: R 15,000
• View Details
Get extra R 3,750 off
USE CODE: SSPD25

Get extra R 550 off
USE CODE: SSPD25

More Questions On Algebra