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Number Theory Level pending
  • If ( 3 ( 230 + t ) ) 2 = 492 a 04 ‾ {(3(230+t))}^{2} = \overline{492a04} , find the value of a a


The answer is 8.

Converti K by Converti K , 25, USA

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1 solution

Converti K
May 28, 2016

Since ( 3 ( 230 + t ) ) 2 = 9 ( 230 + t ) 2 \left( 3\left( 230+t \right) \right) ^{ 2 }=9\left( 230+t \right) ^{ 2 } , 492 a 04 ‾ \overline { 492a04 } is divisible by 9.

Therefore, 4 + 9 + 2 + a + 0 + 4 {4+9+2+a+0+4} is divisible by 9. 19 + a {19+a} can be divided by 9.

∴ a = 8 \therefore {a=8}

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