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My Persian friend said:

I will meet you in New York on my birthday.

But I can't remember her birthday! I only found this riddle related to her birthday in old chats.

$(y+z)/y = (y)/z = (A+10)/10 $

$x_1 =2,x_2 =3,x_3 =5,x_4 =7,... => B=x_1x_6x_{16}$

متولد شده ام B/A من در تاریخ

translation:

I was born in B/A

Can you tell me when I will meet her in New York?

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You will meet her on

September 9

because

The first equation is about golden ratio: $(y+z)/y=y/z=(1+\sqrt5)/2\approx1.618$, so $A\approx6.18$.
The second equation is about primes: $x_i$ represents the $i$th prime, so $B=2\cdot13\cdot53=1378$.
Since your friend is Persian, she is probably wrote her birth date in Persian calendar: 1378/6/18. It corresponds to 1999/9/9 in Gregorian calendar. So, her birthday is on September 9th.

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    $\begingroup$ Why truncate at 6.18 exactly? Why not 6.1, or 6.2 with rounding? (Sorry for putting this comment here, this is not a problem in the answer, but since there are some un-rot13able mild spoilers here, I didn't want to put it too near the question.) $\endgroup$
    – Bass
    Commented Feb 14, 2022 at 13:34
  • $\begingroup$ Because the golden ratio is often known as 1.618, not 1.62. $\endgroup$
    – Marzieh Mousavi
    Commented Oct 10, 2022 at 10:48

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