Given-function-f-4567-321567-567-321-888-f-32156-12062-156-120-276-find-the-value-of-f-20-22-21-

Question Number 198447 by cortano12 last updated on 20/Oct/23

Given function

f (4567, 321567) = 567 + 321 = 888 .

f (32156, 12062) = 156 + 120 = 276

find the value of

f (\frac{20^{22}}{21}) .

Commented by mr W last updated on 20/Oct/23

t h e g i v e n f u n c t i o n i s f (x, y), b u t y o u

a r e a s k i n g f (a) = ?

i t m a k e s n o s e n s e t o m e .

Commented by Rasheed.Sindhi last updated on 20/Oct/23

s i r, I t h i n k c o m m a i s

d e c i m a l s e p a r a t e r h e r e .

Commented by cortano12 last updated on 20/Oct/23

the questions mean if

f (\frac{157683}{321}) = f (491, 785047) = 491 + 785

Commented by mr W last updated on 20/Oct/23

o k . “,^{″} = “ .^{″}

Commented by Rasheed.Sindhi last updated on 20/Oct/23

f (\frac{157683}{321}) = f (491, 785047) = 491 + 785

B u t \frac{157683}{321} = 491.224299 \neq 491, 785047

Answered by Rasheed.Sindhi last updated on 20/Oct/23

f (4567, 321567) = 567 + 321 = 888

f (32156, 12062) = 156 + 120 = 276

f (\frac{20^{22}}{21}) = ?

f (\frac{20^{22}}{21}) = ⌊ \frac{20^{22}}{21} ⌋ m o d 1000

+ ⌊ \frac{20^{22}}{21} \times 1000 ⌋ m o d 1000

∵ \frac{20^{22}}{21} = \frac{2^{22}}{21} \times 10^{22}

= ⌊ \frac{2^{22}}{21} \times 10^{22} ⌋ m o d 10^{3} + ⌊ \frac{2^{22}}{21} \times 10^{25} ⌋ m o d 10^{3}

= 619 + 47 = 666

C o n t i n u e

Answered by MM42 last updated on 20/Oct/23

20^{22} \overset{21}{\equiv} 1 \Rightarrow 20^{22} = 21 k + 1; k = a b c \dots 619

\Rightarrow \frac{20^{22}}{21} = \frac{21 \times a b c . . 619 + 1}{21} = a b c . . 619 + 0.476 . .

\Rightarrow f (\frac{20^{22}}{21}) = 619 + 47 = 666 ✓

Commented by cortano12 last updated on 20/Oct/23

how to get k = abc \dots 619 ?

Commented by MM42 last updated on 20/Oct/23

20^{22} - 1 = a_{1} . . a_{n} 9 \dots 999 = 21 k

i f k = a b c \dots x y z \Rightarrow 21 \times \dots x y z = \dots 999

\Rightarrow z = 9 \Rightarrow 21 \times \dots x y 9 = \dots 999

\underset{⏟}{}

y + 8 = 9 \Rightarrow y = 1

\Rightarrow 21 \times \dots x 19 = \dots 999

x + 3 = 9 \Rightarrow x = 6

\Rightarrow k = a b c \dots 619 ✓

\underset{⏟}{}

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